Answer to Question #50899 in Differential Equations for Nayan Jyoti Das

Question

5. Apply the method of variations of parameters to solve the following differential equations:

a) x^2 y'' + x y' - y = x^2 e^x

b) y'' + a^2 y = cosec ax

c) Solve the equation d^2 y / d x^2 - cot x dy/dx - sin^2 xy = cos x - cos^3 x by changing the independent
variable.