# Question:pdsolve/Solve for derivatives algebraically (without integrating)

## Question:pdsolve/Solve for derivatives algebraically (without integrating)

Maple

Hi,

I have a question regarding pdsolve, or Solve from the PDEtools package. I have a set of equations relating partial derivatives, and I'd like to isolate certain terms without explicitly known the functions. I can do this for a single equation, but not multiple ones. I'm curious if Maple can currently handle a system of eqns like these easily, since I will be increasing the number of eqns in the future. Here's the code

 > restart;
 > PDEtools:-declare(H=H(x,y,t)):
 (1)
 > eq1:= H[tt](x,y,t) = H[xx](x,y,t) + H[yy](x,y,t);
 (2)
 > eq2 := diff(H[tt](x,y,t), t) = diff(H[tx](x,y,t), x) + diff(H[ty](x,y,t), y);
 (3)
 > eq3 := diff(H[tx](x,y,t), t) = diff(H[xx](x,y,t), x) + diff(H[xy](x,y,t), y);
 (4)
 > eq4 :=diff(H[ty](x,y,t), t) = diff(H[xy](x,y,t), x) + diff(H[yy](x,y,t), y);
 (5)
 > PDEtools:-Solve(eq3, H[xy]);
 (6)
 > PDEtools:-Solve({eq1, eq2, eq3, eq4}, H[xy]);
 >
 >