DSolve with conditions in Mathematica

Question

I would like to solve this equation in Mathematica :

DSolve[{p'[r] == 1/((r^2)*(((R - S)/(R^3)) - (1/(r^2)*(1 - S/r)))^(1/2))}, p[r], r]

but I have some supplementary conditions:

• S is a strictly positive real
• R > 3*sqrt(3)*S/2
• I want the solution over the interval r in ]R, +infinity]

I am a beginner with Mathematica so how to specify these conditions ?

Answer 1

Your existing code appears to produce a solution (albeit large) on Mathematica 8

sol = DSolve[{p'[r] == 
1/((r^2)*(((R - S)/(R^3)) - (1/(r^2)*(1 - S/r)))^(1/2))}, p[r], r]

You can add the additional constraints on the solution, as part of the simplification. It doesn't appear to make a significant difference. Were you expecting something different?

Simplify[sol, {S, R} \[Element] Reals && S > 0 && R > 3*sqrt (3)*S/2]

Minor Correction

FullSimplify[sol, {S, R} \[Element] Reals && S > 0 && R > 3*sqrt (3)*S/2]

Appears to simplify some of the terms, but only a little.