Question

Find the Wronskian of a given set {y1, y2} of solutions of y"+3(x^2+1)y'-2y=0, given that W(pi)=0.

Answer 1

@SithsAndGiggles

Answer 2

Are you given particular solutions \(y_1\) and \(y_2\)?

Answer 3

No.

Answer 4

@SithsAndGiggles

Answer 5

This seems to be a problem regarding Abel's theorem: http://en.wikipedia.org/wiki/Abel%27s_identity#Statement_of_Abel.27s_identity

Answer 6

Unless I'm missing something, the fact that \(W(y_1,y_2)(\pi)=0\) would suggest that \(W(y_1,y_2)=0\) as well...

Answer 7

But how to find the solutions of y"+3(x^2+1)y'-2y=0?

Answer 8

You're not looking for the solutions, you're asked to find the Wronskian of the solutions.

See this link for a short discussion on Abel's theorem (at the bottom of the page): http://tutorial.math.lamar.edu/Classes/DE/Wronskian.aspx

Answer 9

Now I get it! I was lost because I thought that I have to find the solutions of y"+3(x^2+1)y'-2y=0. No wonder I couldn't get the right answer that way. Thank you for the link, it helped me a lot.