Use variation of parameters to find the general solution to the following differential equation. x^2y'' - 3xy' + 4y = x^2 ln(x)

Question.

Use variation of parameters to find the general solution to the following differential equation.

x²y'' - 3xy' + 4y = x² ln(x)

Hint: The solution to the homogeneous problem is y_h = c₁x² + c₂x²ln(x)

Solution:

Solve the following Cauchy-Euler equation x^2y'' + 5xy' - 5y = 0

Question.

Solve the following Cauchy-Euler equation x²y'' + 5xy' - 5y = 0