Integral Calculus

Question

Hi! I was wondering how you would antidifferentiate this: x^3+(1/y)(dy/dx)

Answer 1

The method is to separate variables. The expression x³ + (1/y)dy/dx = 0

is -x³ = (1/y)dy/dx or -x³ dx = (1/y) dy

Integrating, you obtain ln(y) = -(1/4)x⁴ + C or y = Ke^(-x4/4)

Where C & K are constants.