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?
DSolve[(D[R[r, t], t])^2/(2*c) - (G*M1[r, z])/(c^2* R[r, t]) - (\[Lambda]*(R[r, t])^2)/3 - E1[r] == 0, R[r, t], t]
$\endgroup$f
in your functionM1[r_]
? a unknown function? $\endgroup$