Problems On Euler's Equation

Problems on Euler's Equation:

1. Solve

Solution: Given (x²D² 4xD 2)y = x logx ...........(1)

            Consider: x = e^z, (or) z = logx

            ∴ x D = θ

           x²D² = θ(θ-1)

Complete Solution is y = C.F P.I

2. Solve ((x²D² - 3xD 4)y = x²

Solution: Given ((x²D² - 3xD 4)y = x²

Complete Solution is