Question

Verify that all members of the family y=(c-x^2)^(-1/2) are solutions of the differential equation y'=xy^3. Can anyone help me with this please?

Answer 1

See below.

Explanation:

`y = (c - x^2)^(-1/2)`

`y' = -1/2 * (c - x^2)^(-3/2) * (-2x)`

`y^3 = (c - x^2)^(-3/2)`

`(y')/(y^3) = +x`