2nd Order Linear ODE w/ nonconstant coefficient

[Valour549]

xy'' + 2xy' - y = 0

Honestly no clue where to start, Wolfram Alpha gives a rather complex answer lol (http://www.wolframalpha.com/input/?i=xy''+2xy'-y=0)

 

[Inventive]

The answer in wolfram alpha is written in a compact form using the substitution e^2x. If the left hand side of the equation is solved implicitly you should get a answer to that portion of their answer that will look similar to the equation that you started with

 

[ModestyKing]

My graduate math for physicists course has been using the Frobenius method for ODEs like that. http://mathworld.wolfram.com/FrobeniusMethod.html