(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Solve the differential equation dy/dx = 3x^{2}(1+y^{2})^{3/2}

2. Relevant equations

3. The attempt at a solution

So far this is what I have (I'm almost finished) -

∫dy/(1+y)^{3/2}= ∫3x^{2}dx

Let y = tan(u) , dy = sec^{2}(u)

Then (1+y^{2})^{3/2}= (tan^{2}(u)+1)^{3/2}= sec^{3}(u) and u = tan^{-1}(y)

∫cos(u)du = ∫3x^{2}dx

sin(u)+c = x^{3}+c

sin(tan^{-1}(y)) = x^{3}+C

One question here, how do I simplify the left-hand side? I seem to have forgotten. Thanks!

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# Seperable differential equations question

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