Question

Solve `x^2 y dy/dx-x^2=1` ?

Solve `x^2 y dy/dx-x^2=1`

Answer 1

The general solution is `y=+-sqrt((-2+2x^2+2Cx)/x)`

Explanation:

This is a first order separable ODE

`x^2ydy/dx-x^2=1`

Dividing by `x^2`

`ydy/dx-1=1/x^2`

`ydy/dx=1/x^2+1`

`ydy=(1/x^2+1)dx`

Integrating both sides

`intydy=int(1/x^2+1)dx`

`1/2y^2=-1/x+x+C`

`y^2=-2/x+2x+2C`

`y^2=(-2+2x^2+2Cx)/x`

`y=+-sqrt((-2+2x^2+2Cx)/x)`