I'm trying to solve the following ode:

[-5*e4(r)*E+3*r*e5(r)*dE-5/3*r*e8(r)*dE+2*e7(r)*E+3*e1(r)*E-4/3*r*e2(r)*dE = 0, 1/3*1/r*(3*r^2*e5(r)*dE-6*r*e4(r)*E-12*M*e7(r)*E+10*M*r*e8(r)*dE-3*r^2*e1(r)*dE+6*M*e4(r)*E-3*M*r*e5(r)*dE+6*r^2*e4(r)*dE+8*M*r*e2(r)*dE-18*M*e1(r)*E-r^2*e2(r)*dE+6*r*e7(r)*E-5*r^2*e8(r)*dE) = 0, 1/3*r*(4*e7(r)*E-5*r*e8(r)*dE-4*e4(r)*E+5*r*e5(r)*dE) = 0, r^2*e2(r)*dE-2*r*e1(r)*E+1/3*r^2*e4(r)*dE+2/3*r^2*e7(r)*dE-8/3*M*e7(r)*E+10/3*M*r*e8(r)*dE+2/3*r*e4(r...

So I've solved this system of ODEs already in a certain gauge where h[r](r) was set to zero, and my answer was consistent with a previously calculated solution, but now I'm trying to do it with a non-zero h[r](r).

The previous result Maple easily solved with dsolve, but puting that in this time, I get:

ode := [-1/2*(4*h[v](r)*r+4*h[r](r)*r-2*diff(h[v](r),`$`(r,2))*r^3-2*h[2](r)*6-2*h[r](r)*6*r+diff(h[2](r),r)*6*r+4*h[2](r)-2*diff(h[2](r),r)*r)/r^3=0,

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...