# Question:Set of complicated PDEs

## Question:Set of complicated PDEs

Maple

Hey everyone.  I'm having problems solving a set of complicated PDEs.  I found a question before that helped me a bit, but the answer was less than ideal.

Here is what I have so far.

pde := [-1/4*Gamma*(Gamma-2)/r^2*G(v,r)+1/r^3*j[v](v,r)*Gamma-1/r*diff(h[vv](v,r),r)-1/r^2*h[vv](v,r)+1/2*1/r^2*diff(j[v](v,r),r)*Gamma = 0, 1/4*f(r)*Gamma*(Gamma-2)*G(v,r)/r^2+1/r*f(r)*diff(h[vv](v,r),r)+1/r*diff(h[vv](v,r),v)-1/r^2*f(r)*diff(j[v](v,r),r)*Gamma-1/r^2*diff(j[v](v,r),v)*Gamma+1/2*(2*f(r)+Gamma)*h[vv](v,r)/r^2-1/2*Gamma*(-1+3*f(r))*j[v](v,r)/r^3 = 0, -1/2*(Gamma-2)*diff(G(v,r),r)+diff(j[v](v,r),`\$`(r,2))-2/r^2*j[v](v,r) = 0, -1/2*(Gamma-2)*diff(G(v,r),v)-f(r)*diff(j[v](v,r),`\$`(r,2))-diff(j[v](v,r),r,v)+diff(h[vv](v,r),r)+2/r*diff(j[v](v,r),v)+2*(f(r)-1)*j[v](v,r)/r^2 = 0, (-r^2*diff(h[vv](v,r),`\$`(r,2))+diff(j[v](v,r),r)*Gamma-2*r*diff(h[vv](v,r),r))/r^2 = 0, -2*r^2*diff(G(v,r),r,v)-r*f(r)*diff(G(v,r),r)+2*diff(j[v](v,r),r)-2*r*diff(G(v,r),v)-r^2*f(r)*diff(G(v,r),`\$`(r,2))-r*diff(G(v,r),r) = 0]

> DEtools[rifsimp](pde,[G(v,r),h[vv](v,r),j[v](v,r)]);

TABLE([Solved = [G(v,r) = 0, h[vv](v,r) = 0, j[v](v,r) = 0], Pivots = [-1+diff(f(r),r)*r+f(r) <> 0, Gamma-2 <> 0, Gamma <> 0], Case = [[(-1+diff(f(r),r)*r+f(r))*(Gamma-2) <> 0, diff(G(v,r),r)], [Gamma <> 0, j[v](v,r)]]])

As you can see Maple gave me zeroes for everything.  Can someone give me a hint on what I'm doing wrong?  I already know what the answer is, I just want to make sure that I can reproduce them by solving the equations in Maple.  Thanks.

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