Solve x2ydydx−x2=1 ?

Question

Solve x2ydydx−x2=1 ?

Answer 1

x²y dy = (1+x²)dx

y dy = (1/x² + 1) dx

 

Now you can antidifferentiate each side, etc...

Answer 2

I assume you meant to say 

 

x²ydy/dx - x² = 1

 

If x ≠ 0, you can divide both sides by x² and get a separable equation.

 

ydy/dx - 1 = 1/x²

 

ydy/dx = 1 + 1/x²

 

ydy = (1 + 1/x²)dx

 

∫ydy = ∫(1 + 1/x²)dx

 

y²/2 = x - 1/x + c

 

y = √[2(x - 1/x + c)]