pdsolve(y(p_,t_)+y(q_,x_)+d_,y_):= if(hasnot(d,y), pdsolve(y(p,t)+y(q,x),y)+if(has(d,t),if(has(d,x), psolution(1,p,0,-d,y,t,t,p)+psolution(1,q,0,-d,y,t,x,p), -int(d,t,p) ), -int(d,x,q) ), block(f:=dsolve(-d,y,x,q),if(p<=1 and q<=1 and hasnot(d,t),replace(replace(f, C_1,C_1*(1+t^p/p!-x^q/q!)),c_1,c_1*(1+t^p/p!-x^q/q!)),f )) ); pdsolve(y(p_,t_)+b_*y(q_,x_)+d_,y_):= if(hasnot(b,d,y), pdsolve(y(p,t)+b*y(q,x),y)+if(has(d/b,t),if(has(d,x), psolution(1,p,0,-d,y,t,t,p)+psolution(b,q,0,-d,y,t,x,p), -int(d,t,p) ), -int(d/b,x,q) ), block(f:=dsolve(-d/b,y,x,q),if(p<=1 and q<=1 and hasnot(d,t),replace(replace(f, C_1,C_1*(1+t^p/p!-int(1/b,x,q))),c_1,c_1*(1+t^p/p!-int(1/b,x,q))),f )) ); pdsolve(f_*y(p_,t_)+y(q_,x_)+d_,y_):= if(hasnot(d,f,y), if(hasnot(f,x),C_1*(int(1/f,t,p)-x^q/q!),0)+if(hasnot(f,t),C_1*(t^p/p!-int(f,x,q)),0)+gsolution(0,y,t,p)+gsolution(0,y,x,q) +if(has(d,t),if(has(d,x), psolution(1/f,p,0,-d/f,y,t,t,p)+psolution(1/f,q,0,-d/f,y,t,x,p), -int(d/f,t,p) ), -int(d,x,q) ), if(hasnot(d,t), dsolve(-d,y,x,q)) ); pdsolve(f_*y(p_,t_)+b_*y(q_,x_)+d_,y_):= if(hasnot(b,d,f,y), if(hasnot(f,x) and hasnot(b,t),C_1*(int(1/f,t,p)-int(1/b,x,q)),0)+if(hasnot(f,t) and hasnot(b,x),C_1*(int(b,t,p)-int(f,x,q)),0)+gsolution(0,y,t,p)+gsolution(0,y,x,q) +if(has(d,t),if(has(d,x), psolution(1/f,p,0,-d/f,y,t,t,p)+psolution(b/f,q,0,-d/f,y,t,x,p), -int(d/f,t,p) ), -int(d/b,x,q) ), if(hasnot(d,t), dsolve(-d/b,y,x,q)) ); #pdsolve(y(1,t_)+y(1,x_)+d_,y_):= replace(replace(dsolve(-d,y,x,1),C_1,C_1+C_2*(t-x)),c_1,C_1+C_2*(t-x)); #pdsolve(y(1,t_)+b_*y(1,x_)+d_,y_):= if(hasnot(b,d,t),replace(replace(dsolve(-d/b,y,x,1), C_1,C_1+C_2*(t-int(1/b,x))),c_1,C_1+C_2*(t-int(1/b,x))) ); #pdsolve(y(p_,t)+a_*y(q_,x_)+d_,y_):= if(hasnot(d,y), if(a<0, C_3*exp(t+x/(-a)^(1/q)),0)+C_1+C_2*(t^p/p!-int(1/a,x,q)) -if(has(d,t),if(has(d,x),if(isinteger(q), psolution(-a,1,0,d,y,t,x,p), psolution(0,d,p,x,q)/a), int(d,t,p) ), int(d/a,x,q) )); #pdsolve(y(1,t)+a_*y(1,x)+d_,y_):= if(has(d,x) and hasnot(d,t), C_1+C_2*F(t-x/a)+expand(int(replace(-d,t,t-x/a+z/a)*replace(-d,x,z),z,0,x)/a) ); #pdsolve(y(p_,t)+y(q_,x_)+b_*y+d_,y):= if(hasnot(d,y), if(isconstant(b), C_3*(exp((-b)^(1/p)*t)+exp((-b)^(1/q)*x))*(t^p/p!-x^q/q!),0)+gsolution(-b,y,t,p)+gsolution(-b,y,x,q) +if(has(d,t), if(has(d,x), psolution(1,-1,q,-b,-d,p,t,x,q),psolution(-b,-d,y,t,p) ), psolution(-b,-d,y,x,q) )); #pdsolve(y(p_,t)+a_*y(q_,x_)+b_*y+d_,y):=if(hasnot(d,y), if(isconstant(a,b), C_3*(exp((-b)^(1/p)*t)+exp((-b/a)^(1/q)*x))*(t^p/p!-x^q/q!/a),0)+gsolution(-b,y,t,p)+gsolution(-b/a,y,x,q) +if(has(d,t), if(has(d,x), psolution(a,0,q,-b,-d,p,t,x,q),psolution(-b,-d,y,t,p) ), psolution(-b/a,-d/a,y,x,q) )); pdsolve(y(p_,t)+y(q_,x_)+y+d_,y):= if(hasnot(d,y), if(p<=1,(1+t^p/p!-x^q/q!),1)*gsolution(-1,y,t,p)+if(q<=1,(1+t^p/p!-x^q/q!),1)*gsolution(-1,y,x,q) +if(has(d,t),if(has(d,x), psolution(1,p,-1,-d,y,t,t,p)+psolution(1,q,-1,-d,y,t,x,p),psolution(-1,-d,y,t,p) ), psolution(-1,-d,y,x,q) )); pdsolve(y(p_,t)+y(q_,x_)+b_*y+d_,y):= if(hasnot(d,y), if(p<=1,1+t^p/p!-x^q/q!,1)*if(hasnot(b,x),gsolution(-b,y,t,p),0)+if(q<=1,1+t^p/p!-x^q/q!,1)*if(hasnot(b,t),gsolution(-b,y,x,q),0) +if(has(d,t),if(has(d,x), psolution(1,p,-b,-d,y,t,t,p)+psolution(1,q,-b,-d,y,t,x,p),psolution(-b,-d,y,t,p) ), psolution(-b,-d,y,x,q) )); pdsolve(y(p_,t)+a_*y(q_,x_)+y+d_,y):= if(hasnot(a,d,y), if(p<=1,1+t^p/p!-int(1/a,x,q),1)*gsolution(-1,y,t,p)+if(q<=1,1+t^p/p!-int(1/a,x,q),1)*if(hasnot(a,t),gsolution(-1/a,y,x,q),0) +if(has(d,t),if(has(d,x), psolution(1,p,-1,-d,y,t,t,p)+psolution(a,q,-1,-d,y,t,x,p),psolution(-1,-d,y,t,p) ), psolution(-1/a,-d/a,y,x,q) )); pdsolve(y(p_,t)+a_*y(q_,x_)+b_*y+d_,y):=if(hasnot(a,b,d,y), if(p<=1,1+t^p/p!-int(1/a,x,q),1)*if(hasnot(b,x),gsolution(-b,y,t,p),0)+if(q<=1,1+t^p/p!-int(1/a,x,q),1)*if(hasnot(a,b,t),gsolution(-b/a,y,x,q),0) +if(has(d,t),if(has(d,x), psolution(1,p,-b,-d,y,t,t,p)+psolution(a,q,-b,-d,y,t,x,p),psolution(-b,-d,y,t,p) ), psolution(-b/a,-d/a,y,x,q) )); pdsolve(y(p_,t)+y(n_,x_)+y(m_,x_)+d_,y_):= if(hasnot(d,y), C_3*(1/p!*t^p-1/m!*x^m)+gsolution(-1,m,0,y,x,n) +if(has(d,t),if(has(d,x), psolution(1,n,1,m,0,d,y,t,x,p), -int(d,t,p)), psolution(-1,m,0,-d,y,x,n)) ); pdsolve(y(p_,t)+a_*y(n_,x_)+y(m_,x_)+d_,y_):= if(hasnot(a,d,y), C_3*(1/p!*t^p-1/m!*x^m)+gsolution(-1/a,m,0,y,x,n) +if(has(d,t),if(has(d,x), psolution(a,n,1,m,0,d,y,t,x,p), -int(d,t,p)), psolution(-1/a,m,0,-d/a,y,x,n)) ); pdsolve(y(p_,t)+y(n_,x_)+b_*y(m_,x_)+d_,y_):= if(hasnot(b,d,y), if(hasnot(b,t), 1/p!*t^p+gsolution(-b,m,0,y,x,n) +if(has(d,t),if(has(d,x), psolution(1,n,b,m,0,1+d,y,t,x,p), -int(d,t,p)), psolution(-b,m,0,-1-d,y,x,n)) )); pdsolve(y(p_,t)+a_*y(n_,x_)+b_*y(m_,x_)+d_,y_):= if(hasnot(a,b,d,y), if(hasnot(b,t), 1/p!*t^p+gsolution(-b/a,m,0,y,x,n) +if(has(d,t),if(has(d,x), psolution(a,n,b,m,0,1+d,y,t,x,p), -int(d,t,p)), psolution(-b/a,m,0,-1/a-d/a,y,x,n) ))); pdsolve(y(p_,t)+y(n_,x_)+b_*y(m_,x_)+xy_+d_,xy_):= gsolution(-1,xy,t,p)*(1+if(isconstant(b),exp((-b)^(1/(n-m))*x),0))+gsolution(-b,m,-1,xy,x,n) +if(has(d,t),if(has(d,x), psolution(1,n,b,m,1,d,y,t,x,p), psolution(-1,-d,xy,t,p)), psolution(-b,m,-1,-d,xy,x,n) ); pdsolve(y(p_,t)+y(n_,x_)+y(m_,x_)+c_*xy_+d_,xy_):= gsolution(-c,xy,t,p)+gsolution(-1,m,-c,xy,x,n) +if(has(d,t),if(has(d,x), psolution(1,n,1,m,c,d,y,t,x,p), psolution(-c,-d,xy,t,p)), psolution(-1,m,-c,-d,xy,x,n) ); pdsolve(y(p_,t)+y(n_,x_)+b_*y(m_,x_)+c_*xy_+d_,xy_):= gsolution(-c,xy,t,p)*(1+if(isconstant(b),exp((-b)^(1/(n-m))*x),0))+gsolution(-b,m,-c,xy,x,n) +if(has(d,t),if(has(d,x), psolution(1,n,b,m,c,d,y,t,x,p), psolution(-c,-d,xy,t,p)), psolution(-b,m,-c,-d,xy,x,n) ); pdsolve(y(p_,t)+a_*y(n_,x_)+y(m_,x_)+c_*xy_+d_,xy_):= gsolution(-c,xy,t,p)*(1+if(isconstant(a),exp((-a)^(1/(m-n))*x),0))+gsolution(-1/a,m,-c/a,xy,x,n) +if(has(d,t),if(has(d,x), psolution(a,n,1,m,c,d,y,t,x,p), psolution(-c,-d,xy,t,p)), psolution(-1/a,m,-c/a,-d/a,xy,x,n) ); pdsolve(y(p_,t)+a_*y(n_,x_)+b_*y(m_,x_)+c_*xy_+d_,xy_):= gsolution(-c,xy,t,p)*(1+if(isconstant(a,b),exp((-b/a)^(1/(n-m))*x),0))+gsolution(-b/a,m,-c/a,xy,x,n) +if(has(d,t),if(has(d,x), psolution(a,n,b,m,c,d,y,t,x,p), psolution(-c,-d,xy,t,p)), psolution(-b/a,m,-c/a,-d/a,xy,x,n) ); pdsolve(y(p_,t)+y(n_,x_)+b_*y(m_,x_)+xy_,xy_):= gsolution(-1,xy,t,p)*(1+if(isconstant(b),exp((-b)^(1/(n-m))*x),0))+gsolution(-b,m,-1,xy,x,n); pdsolve(y(p_,t)+y(n_,x_)+b_*y(m_,x_)+c_*xy_,xy_):= gsolution(-c,xy,t,p)*(1+if(isconstant(b),exp((-b)^(1/(n-m))*x),0))+gsolution(-b,m,-c,xy,x,n); pdsolve(y(p_,t)+a_*y(n_,x_)+y(m_,x_)+c_*xy_,xy_):= gsolution(-c,xy,t,p)*(1+if(isconstant(a),exp((-a)^(1/(m-n))*x),0))+gsolution(-1/a,m,-c/a,xy,x,n); pdsolve(y(p_,t)+a_*y(n_,x_)+b_*y(m_,x_)+xy_,xy_):= gsolution(-1,xy,t,p)*(1+if(isconstant(a,b),exp((-b/a)^(1/(n-m))*x),0))+gsolution(-b/a,m,-1/a,xy,x,n); pdsolve(y(p_,t)+a_*y(n_,x_)+b_*y(m_,x_)+c_*xy_,xy_):= gsolution(-c,xy,t,p)*(1+if(isconstant(a,b),exp((-b/a)^(1/(n-m))*x),0))+gsolution(-b/a,m,-c/a,xy,x,n); pdsolve(y(q_,t_)+y(q_,x_)+xy_^n_,xy_):= (-2fallingfactorial(q/(1-n),q))^(1/(n-1))*(C_1+t+x)^(q/(1-n)) ; pdsolve(y(q_,t_)+y(q_,x_)+b_*xy_^n_,xy_):= if(isconstant(b), (-2/b*fallingfactorial(q/(1-n),q))^(1/(n-1))*(C_1+t+x)^(q/(1-n)) ); pdsolve(y(q_,t_)+a_*y(q_,x_)+b_*xy_^n_,xy_):= if(isconstanta,(b), (-(1+a)/b*fallingfactorial(q/(1-n),q))^(1/(n-1))*(C_1+t+x)^(q/(1-n)) ); pdsolve(xy_+y(p_,t)+y(q_,x_),xy_):=if(p<=1,1+t^p/p!-x^q/q!,1)*gsolution(-1,xy,t,p) +if(q<=1,1+t^p/p!-x^q/q!,1)*gsolution(-1,xy,x,q); pdsolve(a_*xy_+y(p_,t)+y(q_,x_),xy_):=if(p<=1,1+t^p/p!-x^q/q!,1)*if(hasnot(a,x),gsolution(-a,xy,t,p),0) +if(q<=1,1+t^p/p!-x^q/q!,1)*if(hasnot(a,t),gsolution(-a,xy,x,q),0); pdsolve(xy_+y(p_,t)+c_*y(q_,x_),xy_):=if(p<=1,if(hasnot(c,x),1+int(c,t,p)-x^q/q!,1+t^p/p!-int(1/c,x,q)),1)*gsolution(-1,xy,t,p) +if(q<=1,1+t^p/p!-int(1/c,x,q),1)*if(hasnot(c,t),gsolution(-1/c,xy,x,q),0); pdsolve(a_*xy_+y(p_,t)+c_*y(q_,x_),xy_):=if(p<=1,if(hasnot(c,x),1+int(c,t,p)-x^q/q!,1+t^p/p!-int(1/c,x,q)),1)*if(hasnot(a,x),gsolution(-a,xy,t,p),0) +if(q<=1,if(hasnot(c,x),1+int(c,t,p)-x^q/q!,1+t^p/p!-int(1/c,x,q)),1)*if(hasnot(a/c,t),gsolution(-a/c,xy,x,q),0); pdsolve(xy_+b_*y(p_,t)+c_*y(q_,x_),xy_):=if(hasnot(b,x),gsolution(-1/b,y,t,p),0)*if(p<=1 and hasnot(c,t),(1+int(1/b,t,p)-int(1/c,x,q)),1) +if(hasnot(c,t),gsolution(-1/c,y,x,q),0)*if(q<=1 and hasnot(b,x),(1+int(1/b,t,p)-int(1/c,x,q)),1); pdsolve(a_*xy_+b_*y(p_,t)+c_*y(q_,x_),xy_):=if(hasnot(a,b,x),gsolution(-a/b,y,t,p),0)*if(p<=1 and hasnot(c,t),(1+int(1/b,t,p)-int(1/c,x,q)),1) +if(hasnot(a,c,t),gsolution(-a/c,y,x,q),0)*if(q<=1 and hasnot(b,x),(1+int(1/b,t,p)-int(1/c,x,q)),1); pdsolve(y(p_,t)+y(m_,x_)+y(q_,x_),y_):= gsolution(-1,m,0,y,x,q)+gsolution(0,y,t,p)+C_3*(t^p/p!-x^m/m!); pdsolve(y(p_,t)+y(m_,x_)+b_*y(q_,x_),y_):= if(hasnot(b,y), gsolution(-1/b,m,0,y,x,q)+gsolution(0,y,t,p)+C_3*(1/p!*t^p-x^m/m!) ); pdsolve(y(p_,t)+a_*y(m_,x_)+y(q_,x_),y_):= if(hasnot(a,y), gsolution(-a,m,0,y,x,q)+gsolution(0,y,t,p)+if(isconstant(a),C_3*(1/p!*t^p-x^m/m!/a),0) ); pdsolve(y(p_,t)+a_*y(m_,x_)+b_*y(q_,x_),y_):= if(hasnot(a,b,y), gsolution(-a/b,m,0,y,x,q)+gsolution(0,y,t,p)+if(isconstant(a),C_3*(1/p!*t^p-x^m/m!/a),0) ); pdsolve(y(1,t_)+a_*y(2,x_)+b_/x_*y(1,x_),y_):= if(hasnot(a,b,x), gsolution(-b/a/x,1,0,y,x,2)+gsolution(0,y,t,p)+C_3*(t-1/4*a/(a+b)*x^2) ); pdsolve(y(1,t_)+a_*y(2,x_)+a_/x_*y(1,x_),y_):= if(hasnot(a,x), C_1+C_2*log(x)+C_3*(t-1/4/a*x^2)+C_4*Ei(x^2/(4a*t)) ); pdsolve(y(p_,t)+y(q_,x_),y_):= C_1*(t^p/p!-x^q/q!) +gsolution(0,y,t,p)+gsolution(0,y,x,q); pdsolve(y(p_,t)+b_*y(q_,x_),y_):= C_1*(if(hasnot(b,x) and has(b,t),int(b,t,p),t^p/p!) +if(hasnot(b,t), -int(1/b,x,q),-x^q/q!)) +gsolution(0,y,t,p)+gsolution(0,y,x,q); pdsolve(a_*y(p_,t)+y(q_,x_),y_):= if(hasnot(a,t), C_1*(t^p/p!-int(a,x,q)),0) +if(hasnot(a,x), C_1*(int(1/a,t,p)-x^q/q!),0) +gsolution(0,y,t,p)+gsolution(0,y,x,q); pdsolve(a_*y(p_,t)+b_*y(q_,x_),y_):= if(hasnot(a,t) and hasnot(b,x), C_1*(int(b,t,p)-int(a,x,q)),0) +if(hasnot(a,x) and hasnot(b,t), C_1*(int(1/a,t,p)-int(1/b,x,q)),0) +gsolution(0,y,t,p)+gsolution(0,y,x,q); pdsolve(y(p_,t)+a_*b_*y(q_,x_),y_):= if(hasnot(a,t) and hasnot(b,x), C_1*(int(b,t,p)-int(1/a,x,q)),0) +if(hasnot(a,x) and hasnot(b,t), C_1*(int(a,t,p)-int(1/b,x,q)),0) +gsolution(0,y,t,p)+gsolution(0,y,x,q); pdsolve(a_*y(p_,t)+xy_*y(q_,x_),xy_):= if(isconstant(a), -a*fallingfactorial(-p,p)*(C_1+t)^(-p)*(C_2+x)^q/q! ); pdsolve(a_*y(p_,t)+b_*xy_*y(q_,x_),xy_):= if(isconstant(a,b), -a/b*fallingfactorial(-p,p)*(C_1+t)^(-p)*(C_2+x)^q/q! ); pdsolve(y(p_,t)+xy_*y(q_,x_),xy_):= -fallingfactorial(-p,p)*(C_1+t)^(-p)*(C_2+x)^q/q!; pdsolve(y(p_,t)+b_*xy_*y(q_,x_),xy_):= if(isconstant(b), -1/b*fallingfactorial(-p,p)*(C_1+t)^(-p)*(C_2+x)^q/q! ); pdsolve(y(p_,t)+xy_^n_*y(q_,x_),xy_):= (-1)^(1/n)*(C_1+fallingfactorial(-p/n,p)^(-1/p)*t)^(-p/n)*(C_2+fallingfactorial(q/n,q)^(-1/q)*x)^(q/n); pdsolve(y(p_,t)+b_*xy_^n_*y(q_,x_),xy_):=if(isconstant(b),(-1/b)^(1/n)*(C_1+fallingfactorial(-p/n,p)^(-1/p)*t)^(-p/n)*(C_2+fallingfactorial(q/n,q)^(-1/q)*x)^(q/n) ); #pdsolve(y(2,t_)+b_*y(2,x_),y_):= if(isconstant(b), C_1+C_3*(t+x+t^2-x^2/b)+C_2*(sin(x)+cos(x))*if(b>0,(exp(-sqrt(b)*t)+exp(sqrt(b)*t)),(sin(sqrt(-b)*t)+cos(sqrt(-b)*t)) ) ); #pdsolve(y(1,t_)+a_*y(1,x_),y_):= if(hasnot(a,y), if(hasnot(a,x), C_1+C_2*(t-x/a), C_1+t-int(1/a,x) )); #pdsolve(y(1,t_)+a_*y(2,x_),y_):= if(hasnot(a,y), if(hasnot(a,x), C_1+C_2*(t+x-x^2/2/a)+C_3*exp(a*t)*(sin(x)+cos(x))+C_4*erf(x/2/sqrt(-a*t)), C_1+C_2*x+int(-1/a,x,2)+t )); pdsolve(y(p_,t_)+y(2,x_),y_):= C_1+C_2*(t^p/p!+x-x^2/2)+C_3*exp(t)*(sin(x)+cos(x)); pdsolve(y(2,t_)+y(2,x_),y_):= C_1+C_2*(t+x+t^2-x^2)+C_3*(exp(-t)+exp(t))*(sin(x)+cos(x)); pdsolve(y(2,t_)-y(2,x_),y_):= C_1+C_2*(t+x+t^2+x^2)+C_3*(exp(-t)+exp(t))*(exp(-x)+exp(x)); pdsolve(y(2,t_)+y(1,x_),y_):= C_1+C_2*(t+x-t^2/2)+C_3*exp(x)*(sin(t)+cos(t))+C_4*erfi(t/2/sqrt(x)); pdsolve(y(2,t_)-y(1,x_),y_):= C_1+C_2*(t+x+t^2/2)+C_3*exp(-x)*(sin(t)+cos(t))+C_4*erf(t/2/sqrt(x)); pdsolve(y(1,t_)-y(2,x_),y_):= C_1+C_2*(t-x+x^2/2)+C_3*exp(-t)*(sin(x)+cos(x))+C_4*erf(x/2/sqrt(t)); pdsolve(y(p_,t_)+b_*y(1,x_)+c_*y(1,u_),y_):= if(isconstant(b,c), C_1+C_2*(2*t^p/p!-u/c-x/b) ); pdsolve(y(p_,t_)+b_*y(1,x_)+c_*y(1,u_)+f_,y_):= if(isconstant(b,c), psolution(1,p,0,-f,y,t,t,p)+ psolution(b,1,0,-f,y,t,x,p)+psolution(-c,1,0,-f,y,t,u,p)+C_1+C_2*(2*t^p/p!-u/c-x/b) ); pdsolve(y(p_,t_)+b_*y(1,x_)+c_*y(1,u_)+g_*xy_,xy_):= gsolution(-g,xy,t,p)+gsolution(-g/b,xy,x,1)+gsolution(-g/c,xy,u,1); pdsolve(y(p_,t_)+b_*y(1,x_)+c_*y(1,u_)+g_*xy_+f_,xy_):= psolution(1,p,-g,-f,xy,t,t,p)+ psolution(b,1,-g,-f,xy,t,x,p)+psolution(-c,1,-g,-f,xy,t,u,p) +gsolution(-g,xy,t,p)+gsolution(-g/b,xy,x,1)+gsolution(-g/c,xy,u,1); pdsolve(y(p_,t_)+b_*y(1,x_)+c_*y(1,u_)+d_*y(1,v_),y_):= if(isconstant(b,c,d), C_1+C_2*(3*t^p/p!-u/c-x/b-v/d) ); pdsolve(y(p_,t_)+b_*y(1,x_)+c_*y(1,u_)+d_*y(1,v_)+f_,y_):= psolution(1,p,0,-f,y,t,t,p)+ psolution(b,1,0,-f,y,t,x,p)+psolution(-c,1,0,-f,y,t,u,p)+psolution(-d,1,0,-f,y,t,v,p) +if(isconstant(b,c,d), C_1+C_2*(3*t^p/p!-u/c-x/b-v/d),0 ); pdsolve(y(p_,t_)+b_*y(1,x_)+c_*y(1,u_)+d_*y(1,v_)+g_*xy_,xy_):= gsolution(-g,xy,t,p)+gsolution(-g/b,xy,x,1)+gsolution(-g/c,xy,u,1)+gsolution(-g/d,xy,v,1); pdsolve(y(p_,t_)+b_*y(1,x_)+c_*y(1,u_)+d_*y(1,v_)+g_*xy_+f_,xy_):= psolution(1,p,-g,-f,xy,t,t,p)+psolution(b,1,-g,-f,xy,t,x,p)+psolution(-c,1,-g,-f,xy,t,u,p)+psolution(-d,1,-g,-f,xy,t,v,p) +gsolution(-g,xy,t,p)+gsolution(-g/b,xy,x,1)+gsolution(-g/c,xy,u,1)+gsolution(-g/d,xy,v,1); pdsolve(y(p_,t_)+b_*y(2,x_)+c_*y(2,u_),y_):= if(isconstant(b,c), C_1+C_3*(2t^p/p!-x*x/2/b-u*u/2/c)+C_2*exp((b+c)^(1/p)*t)*sin(x)*sin(u) ); pdsolve(y(p_,t_)+b_*y(2,x_)+c_*y(2,u_)+f_,y_):= if(isconstant(b,c), psolution(1,p,0,-f,y,t,t,p)+psolution(b,2,0,-f,y,t,x,p)+psolution(-c,2,0,-f,y,t,u,p) +C_1+C_3*(x+u+4*t^p/p!-u^2/c-x^2/b)+C_2*exp((b+c)^(1/p)*t)*sin(x)*sin(u) ); pdsolve(y(p_,t_)+b_*y(2,x_)+c_*y(2,u_)+g_*xy_,xy_):= gsolution(-g,y,t,p)+gsolution(-g/b,xy,x,2)+gsolution(-g/c,xy,u,2); pdsolve(y(p_,t_)+b_*y(2,x_)+c_*y(2,u_)+g_*xy_+f_,xy_):= psolution(1,p,-g,-f,xy,t,t,p)+psolution(b,2,-g,-f,xy,t,x,p)+psolution(-c,2,-g,-f,xy,t,u,p) +gsolution(-g,y,t,p)+gsolution(-g/b,xy,x,2)+gsolution(-g/c,xy,u,2); pdsolve(y(p_,t_)+b_*y(2,x_)+c_*y(2,u_)+d_*y(2,v_),y_):= if(isconstant(b,c,d), C_1+C_3*(x+u+v+6*t^p/p!-u^2/c-x^2/b-v^2/d)+C_2*exp((b+c+d)^(1/p)*t)*sin(x)*sin(u)*sin(v) ); pdsolve(y(p_,t_)+b_*y(2,x_)+c_*y(2,u_)+d_*y(2,v_)+f_,y_):= psolution(1,p,0,-f,y,t,t,p)+psolution(b,2,0,-f,y,t,x,p)+psolution(-c,2,0,-f,y,t,u,p)+psolution(-d,2,0,-f,y,t,v,p) +if(isconstant(b,c,d),C_3*(x+u+v+6*t^p/p!-u^2/c-x^2/b-v^2/d),0); pdsolve(y(p_,t_)+b_*y(2,x_)+c_*y(2,u_)+d_*y(2,v_)+g_*xy_,xy_):= gsolution(-g,y,t,p)+gsolution(-g/b,xy,x,2)+gsolution(-g/c,xy,u,2)+gsolution(-g/d,xy,v,2); pdsolve(y(p_,t_)+b_*y(2,x_)+c_*y(2,u_)+d_*y(2,v_)+g_*xy_+f_,xy_):= psolution(1,p,-g,-f,xy,t,t,p)+psolution(b,2,-g,-f,xy,t,x,p)+psolution(-c,2,-g,-f,xy,t,u,p)+psolution(-d,2,-g,-f,xy,t,v,p) +gsolution(-g,y,t,p)+gsolution(-g/b,xy,x,2)+gsolution(-g/c,xy,u,2)+gsolution(-g/d,xy,v,2); pdsolve(y(2,t_)+b_*y(2,x_)+c_*y(1,t_)+d_*y(1,x_)+g_*xy_,xy_):= gsolution(-c,-g,y,t,2)*(1+exp(-d/b*x))+gsolution(-d/b,-g/b,y,x,2)*(1+exp(-c*t)); pdsolve(y(2,x_)+b_*y(2,t_)+c_*y(1,x_)+d_*y(1,t_)+g_*xy_,xy_):= gsolution(-c,-g,y,x,2)*(1+exp(-d/b*t))+gsolution(-d/b,-g/b,y,t,2)*(1+exp(-c*x)); pdsolve(y(2,x_)+b_*y(2,t_)+c_*y(1,x_)+d_*y(1,t_)+xy_,xy_):= gsolution(-c,-1,y,x,2)*(1+exp(-d/b*t))+gsolution(-d/b,-1/b,y,t,2)*(1+exp(-c*x)); pdsolve(y(2,x_)+y(2,t_)+c_*y(1,x_)+d_*y(1,t_)+g_*xy_,xy_):= gsolution(-c,-g,y,x,2)*(1+exp(-d*t))+gsolution(-d,-g,y,t,2)*(1+exp(-c*x)); pdsolve(y(2,x_)+y(2,t_)+c_*y(1,x_)+d_*y(1,t_)+xy_,xy_):= gsolution(-c,-1,y,x,2)*(1+exp(-d*t))+gsolution(-d,-1,y,t,2)*(1+exp(-c*x)); pdsolve(a_=b_,y_):=pdsolve(replace(toy(a-b),y(x),y),y); pdsolve(a_):=pdsolve(replace(toy(a),y(x),y),y);