#2;
pdsolve1(y(p_,t_)+b_*y(q_,x_),y_):= if(b<0, C_2*exp((-b)^(1/p)*t+x),0)
	+if(hasnot(b,y), if(q>0, C_1*(if(hasnot(b,t),if(hasnot(b,x),t^p/p!-x^q/q!/b, t^p/p!-int(1/b,x,q)), int(b,t,p)-x^q/q!))
	+if(p>1 and q>1, C_3*t*x,0)+gsolution(0,y,t,p)+gsolution(0,y,x,q),0) );
pdsolve1(y(1,t_)+b_*y(1,x_),y_):= if(has(b,y), if(has(b,x),if(has(b,t),solve(b+d(b,t)/d(b,x),y)), solve(b=(C_1+x)/(C_2+t),y) ),
	if(hasnot(b,t),C_1+C_2*(t-int(1/b,x)), if(hasnot(b,x),C_1+C_2*(x-int(b,t)) )));
#pdsolve1(y(1,t_)+a_*y(2,x_),y_):= if(hasnot(a,t) and hasnot(a,x)),
	int(1/int(1/a,y),y)=C_1-t+x and int(1/int(1/a,y),y)=C_1-t-x );
pdsolve1(y(p_,t_)+a_*b_*y(q_,x_),y_):=  if(hasnot(a,b,y), if(hasnot(a,x) and hasnot(b,t), C_1*(int(a,t,p)-int(1/b,x,q)), if(hasnot(b,x) and hasnot(a,t), C_1*(int(b,t,p)-int(1/a,x,q)) )),
	if(p<=1 and q<=1,
	if(has(b,y), if(hasnot(a,x),solve(b=(C_1+x)/(C_2+int(a,t)),y), if(hasnot(a,t),solve(b=(C_1+int(1/a,x))/(C_2+t),y) )),
	if(has(a,y), if(hasnot(b,x),solve(a=(C_1+x)/(C_2+int(b,t)),y), if(hasnot(b,t),solve(a=(C_1+int(1/b,x))/(C_2+t),y) )) )), 
	a*b=(C_1+x)/(C_2+t) ));
#pdsolve1(y(1,t_)+a_*b_*y(2,x_),y_):= if(hasnot(b,t) and hasnot(a,b,x)),
	int(1/int(1/b,y),y)=C_1-int(a,t)+x and int(1/int(1/b,y),y)=C_1-int(a,t)-x );


#3;
pdsolve1(y(p_,t_)^m_+y(q_,x_)^n_+d_,y_):= if(isconstant(d), C_1+C_2*t^p/p!+(-d-C_2^m)^(1/n)*x^q/q!);
pdsolve1(y(p_,t_)^m_+y(p_,x_)^m_+c_,y_):= if(hasnot(c,t), t+dsolve(y(p,x)^m+c+1,y) );
#pdsolve1(y(p_,t_)^m_+b_*y(p_,x_)^m_+c_,y_):= if(hasnot(b,c,t), t^p/p!+int((-1/b-c/b)^(1/m),x)+gsolution(0,y,x,p) );
pdsolve1(y(p_,t_)^m_+b_*y(p_,x_)^m_+c_,y_):= if(hasnot(c,t), t^p/p!+dsolve(y(p,x)^m+c/b+1/b,y) );

 
pdsolve1(a_*y(p_,t_)+y(q_,x_)+d_,y_):= if(hasnot(a,d,y), if(hasnot(a,x),C_1*(int(1/a,t,p)-x^q/q!),0)
	+if(hasnot(a,t),C_1*(t^p/p!-int(a,x,q)),0)+gsolution(0,y,t,p)+gsolution(0,y,x,q)
	+psolution(1/a,q,0,d/a,y,t,x,p) );
pdsolve1(a_*y(p_,t_)+b_*y(q_,x_)+d_,y_):= if(hasnot(a,b,d,y), if(q<0,dsolve(d(a,x,-q)*y(p,t)+b*y+d(d,x,-q)),
	if(hasnot(d,y), if(isinteger(p) or a<0,C_2*exp((-a)^(1/p)*t+x),0)+psolution(a,q,0,d,y,t,x,p)+if(q>0,C_1,0)+C_3*(if(hasnot(b,x),int(b,t,p),t^p/p!)-if(hasnot(b,t),int(1/b,x,q),x^q/q!) ),
	if(hasnot(a,x) and hasnot(b,t),C_1*(int(1/a,t,p)-int(1/b,x,q)),0)
	+if(hasnot(a,t) and hasnot(b,x),C_1*(int(b,t,p)-int(a,x,q)),0)
	+gsolution(0,y,t,p)+gsolution(0,y,x,q)+if(isconstant(a),psolution(b/a,q,0,d/a,y,t,x,p),psolution(a,p,b,q,0,d,y,x,t)) ))); 
pdsolve1(y(p_,t_)+b_*y(q_,x_)+d_,y_):= if(hasnot(b,d,y), pdsolve(y(p,t)+b*y(q,x),y)+psolution(b,q,0,d,y,t,x,p), 
	if(p==q,if(hasnot(b,d,x), if(isconstant(d), if(p<=1, int((1+b)^(1/p),y)=C_1-d*t-d*x,if(p==2, int(int(-d,y)^(-1/2),y)=sqrt(2/(C_2^2+b*C_1^2))*(C_3+C_2*t+C_1*x) )),
	replace(replace(dsolve(-d/b,y,t,p),C_1,C_1+C_2*(x^q-b*t^p)),c_1,c_1+C_2*(x^q-b*t^p)) ), 
	replace(replace(dsolve(-d/b,y,x,q),C_1,C_1+C_2*(x^q-b*t^p)),c_1,c_1+C_2*(x^q-b*t^p)) ), 
	if(q>1,dsolve(-d,y,t,p),
	if(p>1,dsolve(-d/b,y,x,q),
	dsolve(1-d/b,y,x,q)-t^p/p! ))));
pdsolve1(y(p_,t_)+y(q_,x_)+d_,y_):= if(hasnot(d,y), pdsolve(y(p,t)+y(q,x),y)+psolution(1,q,0,d,y,t,x,p), 
	if(hasnot(d,x),dsolve(-d,y,t,p),
	if(hasnot(d,t),dsolve(-d,y,x,q),
	dsolve(1-d,y,x,q)-t^p/p! )));
pdsolve1(y(p_,t_)+y(p_,x_)+d_,y_):= if(hasnot(d,y), pdsolve(y(p,t)+y(p,x),y)+psolution(1,p,0,d,y,t,x,p), 
	if(hasnot(d,x), if(p>1,replace(replace(dsolve(-d/2,y,t,p),C_1,C_1+x),c_1,c_1+x),
	replace(replace(dsolve(-d,y,t,p),C_1,C_1+C_2*(x^p-t^p)),c_1,c_1+C_2*(x^p-t^p)) ), 
	replace(replace(dsolve(-d,y,x,p),C_1,C_1+C_2*(x^p-t^p)),c_1,c_1+C_2*(x^p-t^p)) )); 


#pdsolve1(a_*b_+y(p_,t_)+c_*y(p_,x_),y_):= if(p<=1 and has(b,y) and hasnot(a,y), int(1/b,y,p)=pdsolve(y(p,t)+c*y(p,x),y)+psolution(c,p,0,a,y,t,x,p)*p!,
	if(p<=1 and has(a,y) and hasnot(b,y), int(1/a,y,p)=pdsolve(y(p,t)+c*y(p,x),y)+psolution(c,p,0,b,y,t,x,p)*p!,
	if(hasnot(b,y), pdsolve(y(p,t)+c*y(p,x),y)+psolution(c,p,0,a*b,y,t,x,p) )));
#pdsolve1(a_*b_+y(p_,t_)+y(p_,x_),y_):= if(p<=1 and has(b,y) and hasnot(a,y), int(1/b,y,p)=c_1+C_1*(t^p-x^p)+psolution(1,p,0,a,y,t,x,p)*p!,
	if(p<=1 and has(a,y) and hasnot(b,y), int(1/a,y,p)=c_1+C_1*(t^p-x^p)+psolution(1,p,0,b,y,t,x,p)*p!,
	if(hasnot(b,y), C_2+C_1*(t^p-x^p)+psolution(1,p,0,a*b,y,t,x,p) )));

#pdsolve1(a_*b_+y(p_,t_)+c_*y(p_,x_),y_):= if(p<=1 and has(b,y) and hasnot(a,y), solve(int(1/b,y,p)=pdsolve(y(p,t)+c*y(p,x),y)+psolution(c,p,0,a,y,t,x,p)*p!,y),
	if(p<=1 and has(a,y) and hasnot(b,y), solve(int(1/a,y,p)=pdsolve(y(p,t)+c*y(p,x),y)+psolution(c,p,0,b,y,t,x,p)*p!,y),
	if(hasnot(b,y), pdsolve(y(p,t)+c*y(p,x),y)+psolution(c,p,0,a*b,y,t,x,p) )));
#pdsolve1(a_*b_+y(p_,t_)+y(p_,x_),y_):= if(p<=1 and has(b,y) and hasnot(a,y), solve(int(1/b,y,p)=c_1+C_1*(t^p-x^p)+psolution(1,p,0,a,y,t,x,p)*p!,y),
	if(p<=1 and has(a,y) and hasnot(b,y), solve(int(1/a,y,p)=c_1+C_1*(t^p-x^p)+psolution(1,p,0,b,y,t,x,p)*p!,y),
	if(hasnot(b,y), C_2+C_1*(t^p-x^p)+psolution(1,p,0,a*b,y,t,x,p) )));

pdsolve1((a_+y_)^n_+z1_+z2_,y_):= if(d(a,x,2)==0 and d(a,t,2)==0, pdsolve(y^n+z1+z2,y)-a );
pdsolve1((a_+b_*y_)^n_+z1_+z2_,y_):= if(isconstant(b) and d(a,x,2)==0 and d(a,t,2)==0, pdsolve(y^n+z1+z2,y)/b^n-a/b );
pdsolve1(c_*(a_+y_)^n_+z1_+z2_,y_):= if(hasnot(c,y) and d(a,x,2)==0 and d(a,t,2)==0, pdsolve(c*y^n+z1+z2,y)-a );
pdsolve1(c_*(a_+y_)+z1_+z2_,y_):= if(hasnot(c,y) and d(a,x,2)==0 and d(a,t,2)==0, pdsolve(c*y+z1+z2,y)-a );
pdsolve1(y(p_,t_)+z1_+z2_,y_):= dsolve(z1+z2,y)+if(hasnot(z1,z2,y),gsolution(0,y,t,p),0);


pdsolve1(y(p1_,t_)+b_*y(p2_,u_)+c_*y(p3_,x_),y_):= if(isconstant(b,c), C_1+C_2*(2*t^p1/p1!-u^p2/p2!/b-x^p3/p3!/c) );
#pdsolve1(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*E(p,(b+c)*t^p)*sin(x)*sin(u) );

pdsolve1(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*(t^p/p!-x^m/m!) );
pdsolve1(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)+C_3*(t^p/p!-if(isconstant(a),x^m/m!/a,psolution(-a,m,0,1,y,x,q))) );
pdsolve1(y(p_,t_)+a_*y(m_,x_)+b_*y(q_,x_),y_):= if(m==q, pdsolve(y(p,t)+(a+b)*y(m,x),y),
	if(hasnot(a,b,y), gsolution(-a/b,m,0,y,x,q)+gsolution(0,y,t,p)+C_3*(t^p/p!-if(isconstant(a),x^m/m!/a,psolution(-a/b,m,0,1/b,y,x,q))) ));


#4;
pdsolve1(a_+y_+z1_+z2_,y_):= if(isconstant(a), pdsolve(y+z1+z2,y)-a );
pdsolve1(a_+b_*y_+z1_+z2_,y_):= if(isconstant(a,b), pdsolve(b*y+z1+z2,y)-a/b );

pdsolve1(y(p_,t_)+y(q_,x_)^n_+d_+f_,y_):= if(hasnot(d,x) and hasnot(f,t), 
	t^p/p!-int(d,t,p)+(-1)^(1+n)*dsolve(y(q,x)^n+f+1,y)+gsolution(0,y,t,p) );
pdsolve1(y(p_,t_)+b_*y(q_,x_)^n_+d_+f_,y_):= if(hasnot(d,x) and hasnot(f,t), 
	t^p/p!-int(d,t,p)+(-1)^(1+n)*dsolve(y(q,x)^n+f+1,y)*b^(-1/n)+gsolution(0,y,t,p) );

pdsolve1(y(p_,t_)+y(q_,x_)^n_+b_*y(m_,x_)+d_,y_):= if(hasnot(d,b,t),if(isconstant(d), dsolve(y(q,x)^n+b*y(m,x),y)-d*t^p/p!+gsolution(0,y,t,p),
	dsolve(y(q,x)^n+b*y(m,x)+d,y)+gsolution(0,y,t,p) ));
pdsolve1(y(p_,t_)+a_*y(q_,x_)^n_+b_*y(m_,x_)+d_,y_):= if(hasnot(a,d,b,t),
	if(isconstant(d), dsolve(y(q,x)^n+b/a*y(m,x),y)-d*t^p/p!+gsolution(0,y,t,p),dsolve(y(q,x)^n+b/a*y(m,x)+d/a,y)+gsolution(0,y,t,p) ));

pdsolve1(y(p_,t_)^m_+y(q_,x_)^n_+b_*y(k_,x_)+d_,y_):= if(hasnot(d,b,t),if(isconstant(d), dsolve(y(q,x)^n+b*y(k,x),y)+(-d)^(1/m)*t^p/p!+gsolution(0,y,t,p),dsolve(y(q,x)^n+b*y(k,x)+d,y) ));
pdsolve1(y(p_,t_)^m_+a_*y(q_,x_)^n_+b_*y(k_,x_)+d_,y_):= if(hasnot(a,d,b,t),
	if(isconstant(d), dsolve(y(q,x)^n+b/a*y(k,x),y)+(-d)^(1/m)*t^p/p!+gsolution(0,y,t,p),dsolve(y(q,x)^n+b/a*y(k,x)+d/a,y) ));


#5;
pdsolve1(a_+y_+z1_+z2_+z3_,y_):= if(isconstant(a), pdsolve(y+z1+z2+z3,y)-a );
pdsolve1(a_+y_+z1_+z2_+z3_+z4_,y_):= if(isconstant(a), pdsolve(y+z1+z2+z3+z4,y)-a );
pdsolve1(a_+b_*y_+z1_+z2_+z3_,y_):= if(isconstant(a,b), pdsolve(b*y+z1+z2+z3,y)-a/b );
pdsolve1(a_+b_*y_+z1_+z2_+z3_+z4_,y_):= if(isconstant(a,b), pdsolve(b*y+z1+z2+z3+z4,y)-a/b );


#0;
pdsolve1(a_):=pdsolve1(toy(a),y);
pdsolve1(a_=b_):=pdsolve1(toy(a-b),y);
pdsolve1(y(p_,t)=b_,y_):=if(hasnot(b,t),if(p>1,dsolve(b,y)+t,dsolve(b-1,y)+t^p/p!));