TiNspire CX CAS: Nonhomogeneous, Nonlinear Cauchy Euler 3. order Differential Equation

To solve a 3. order Cauchy Euler Differential that is Nonhomogeneous and NonLinear you would use the Differential Equations Made Easy at www.TiNspireApps.com and enter the coefficients of the Differential Equations as follows:

As can be seen, the substitution y=x^n allows us to find the zeros of the homogeneous Differential Equation and its solution below. Now, we are after the nonhomogenous solution which involves find the 4 Wronskians W, W1, W2, W3 using the Variation of Parameter method:

After finding the 3 v_i, their integration allows us to find the final solution

Puuh, that was a lot of work…If you want to skip watch all the steps you might just jump straight to the final solution.