Yes, thank you for catching that mistake! I have corrected it now.

[Alfy102]

Homework Statement

If y(1+x²) dy/dx = 2x (1-y²), prove that (1+x²)²(1-y²)=A, where A is constant.

Homework Equations

Separable equations

The Attempt at a Solution

Separate the terms:

y/(1-y²) dy = 2x/(1+x²) dx

Integrating both sides will get:

∫ y/(1-y²) dy = ∫ 2x/(1+x²) dx

Use substitution method for ∫ y/(1-y²) dy:

u = 1-y²
du = -2y dy
-du/2 = y dy

∫ -u/2 du = -1/2 ∫ u du
= (-1/2)*(u²/2)
= -u²/4 + C
= -(1-y²)²/4

Use substitution method for ∫ 2x/(1+x²) dx:

u= 1+x²
du = 2x

∫ 1/u du = ln u + C
= ln (1+x²)


Putting them back together will get:

-(1-y²)²/4 = ln (1+x²)

I'm pretty much unable to continue from here.

 

[CompuChip]

∫ -u/2 du = -1/2 ∫ u du

Don't you mean 1/u there as well?