Question

Solve: d²y/dx² = x + sin x. 

Answer 1

The given differential equation is 

(d²y/dx²) = x + sin x

(d/dx)(dy/dx) = x + sin x

Integrating, we get

dy/dx = (x²/2) - cos x + c₁

Again integrating, we get 

y = (x³/6) – sin x + c₁x + c₂

which is the required solution