Question

Solve the following ordinary differential equation.

dy/dx = (x^3) sec y

Answer 1

$\frac{dy}{dx}=x^3. sec\ y \\\frac{dy}{sec \ y}=x^3dx \\ cos \ ydy=x^3dx$

Integrating both sides, we get

$\int cos \ ydy=\int x^3dx+c \\sin\ y=\frac{x^4}{4}+c$