Using Mathematica, solve the following differential equation by completing the following steps.

$x^2{y}^{\text{'}\text{'}}-9x{y}^{\text{'}}+21y=x^{3}lnx$

a$.$ Find $y_c$ by using the Solve functionality of Mathematica.

b$.$ Find the Wronskian $($W$),$ W$1,$ and W$2$ for the differential equation using matrices.

c$.$ Integrate to find the $y_p$ solution. Use Expand to make it simplify as much as possible.

d$.$ Use DSolve to verify your solution. Use Expand to make it simplify as much as possible.

Please provide coding to answer problem and results from these codes