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


     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 





H(x, y, t)*`will now be displayed as`*H


eq1:= H[tt](x,y,t) = H[xx](x,y,t) + H[yy](x,y,t);

H[tt](x, y, t) = H[xx](x, y, t)+H[yy](x, y, t)


eq2 := diff(H[tt](x,y,t), t) = diff(H[tx](x,y,t), x) + diff(H[ty](x,y,t), y);

diff(H[tt](x, y, t), t) = diff(H[tx](x, y, t), x)+diff(H[ty](x, y, t), y)


eq3 := diff(H[tx](x,y,t), t) = diff(H[xx](x,y,t), x) + diff(H[xy](x,y,t), y);

diff(H[tx](x, y, t), t) = diff(H[xx](x, y, t), x)+diff(H[xy](x, y, t), y)


eq4 :=diff(H[ty](x,y,t), t) = diff(H[xy](x,y,t), x) + diff(H[yy](x,y,t), y);

diff(H[ty](x, y, t), t) = diff(H[xy](x, y, t), x)+diff(H[yy](x, y, t), y)


PDEtools:-Solve(eq3, H[xy]);

H[xy](x, y, t) = Int(diff(H[tx](x, y, t), t)-(diff(H[xx](x, y, t), x)), y)+_F1(x, t)


PDEtools:-Solve({eq1, eq2, eq3, eq4}, H[xy]);

Error, (in pdsolve/sys) the input system cannot contain equations in the arbitrary parameters alone; found equation depending only on {H[tt](x,y,t), H[xx](x,y,t), H[yy](x,y,t)}: H[tt](x,y,t)-H[xx](x,y,t)-H[yy](x,y,t)






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