(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

x^2y''-2xy'+2y=x^3cosx

Find a general solution by using variation of parameters

2. The attempt at a solution

I already solved this one, but I have 4 questions:

1. I found the solutions x and x^2 to the homogeneous equation by inspection. Is this the only way to do it?

2. How about the solutions -x and -x^2? I first tried the solutions x^2 and -x^2, and that gave me 0 as the particular solution...Why can't I choose these two?

3. When calculating the Wronski, how do I know which solution is y1 and y2? I first chose y1 as x^2, and that gave me a different solution...

4. Why are there no constants of integration?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Variation of parameters

**Physics Forums | Science Articles, Homework Help, Discussion**