Question

Solve: \( \left(1+2 x y \cos x^{2}-2 x y\right) d x+\left(\sin x^{2}-x^{2}\right) d y=0 \).

Answer 1

(1 + 2xy cosx² − 2xy) dx + (sinx² − x²) dy = 0

(1 + 2xy cos(x²) − 2xy) dx + (sin(x²) − x²) dy = 0

First order linear Ordinary Differential Equation

A first order linear ODE has the form of y′(x) + p(x)y = q(x)

Let y be the dependent variable, Divide by dx: