Differential Equation help

Question

I have a differential equation that looks like this:

 DSolve[(D[R[r, t], t])^2/(2*c) - (G*M1[r, z])/(
   c^2*R[r, t]) - (λ*(R[r, t])^2)/3 - E1[r] == 0, ... "boundary conditions etc go here"]

I need to get R[r, t] using my values of E1[r] and M1[r]. However, my M1[r] is defined as:

M1[r_] :=  NIntegrate[(1 + f*Exp[-(r/y)^2])*(r)^2, r]

Herein lies the problem. I realise that DSolve uses Integrate internally, but the function I want it to solve has an NIntegrate in it and this causes problems. I'm not sure how else to evaluate an error function.

Any ideas?

Answer 1

Not knowing what the actual differential equation is, I can only point out one obvious problem: you should define

Clear[r,f,y];
M1[r_] = Integrate[(1 + f*Exp[-(r/y)^2])*(r)^2, r]

instead of using := NIntegrate because you seem to be looking for an indefinite integral there. For numerical integration you have to specify integration limits. The Clear is just added for safety before I define the function with = so that the integral will be done at that time, once and for all.