Solve the linear differential equation x dy/dx - y =(x-1)e^x.

Question

Solve the linear differential equation x\(\frac{dy}{dx}\)−y=(x−1)e^x.

Answer 1

Given, x\(\frac{dy}{dx}\) – y = (x – 1)e^x, dividing both sides by x ,we get

Solution is

y × IF = ∫Q(IF)dx + c