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mathwolfram-mathematicasymbolic-math

DSolve with conditions in Mathematica

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 ?

Solution

  • 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.