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

If y(1+x^{2}) dy/dx = 2x (1-y^{2}), prove that (1+x^{2})^{2}(1-y^{2})=A, where A is constant.

2. Relevant equations

Separable equations

3. The attempt at a solution

Separate the terms:

y/(1-y^{2}) dy = 2x/(1+x^{2}) dx

Integrating both sides will get:

∫ y/(1-y^{2}) dy = ∫ 2x/(1+x^{2}) dx

Use substitution method for ∫ y/(1-y^{2}) dy:

u = 1-y^{2}

du = -2y dy

-du/2 = y dy

∫ -u/2 du = -1/2 ∫ u du

= (-1/2)*(u^{2}/2)

= -u^{2}/4 + C

= -(1-y^{2})^{2}/4

Use substitution method for ∫ 2x/(1+x^{2}) dx:

u= 1+x^{2}

du = 2x

∫ 1/u du = ln u + C

= ln (1+x^{2})

Putting them back together will get:

-(1-y^{2})^{2}/4 = ln (1+x^{2})

I'm pretty much unable to continue from here.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Separable equations proving

**Physics Forums | Science Articles, Homework Help, Discussion**