I am trying to solve(adsbygoogle = window.adsbygoogle || []).push({});

[tex]x^2y'' + xy' = 0[/tex]

I know that two solutions that work, by inspection are

[tex]y_1 = c_1[/tex]

and

[tex]y_2 = c_2ln(x)[/tex]

where [tex]c_1[/tex] and [tex]c_2[/tex] are just arbitrary constants.

However I was hoping I would be able to find a more systematic way to solve it. I can get the constant solution by the method of Frobenius, but when I tried to get the natural log solution using the Wronskian, I wasn't able to get it.

I ended up with the second solution being the integral of a Gaussian or something of that sort. I know the Wronskian method is always supposed to work for DEQ's of this type. Where am I going wrong? Can someone show me how to use the Wronskian and the constant solution to get the natural log solution?

(Also why do my LaTeX expressions look funny)

Thanks for the help

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