Use the guess-and-test method to find the power series expansion centered at t = 0 for t...

Use the guess-and-test method to find the power series expansion centered at t = 0 for the general solution up to degree four, that is, up to and including the t⁴ term. (You may find the general solution using other methods and then find the Taylor series centered at t = 0 to check your computation if you like.)