My Math Forum 2nd order differential equation - variation of parameters

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 May 8th, 2014, 12:26 PM #1 Newbie   Joined: Oct 2013 Posts: 29 Thanks: 1 2nd order differential equation - variation of parameters Hello, I have a short question regarding variation of parameters. Suppose we have a differential equation $\displaystyle (x-1)y''-xy'+y=(x-1)^2$, whose fundamental system is $\displaystyle \{x,e^{x}\}$ Now, my question is, if I am to search for the particular solution with the variation of parameters method, should I divide the whole equation by (x-1) first? I.E. will the system of equations with the fundamental matrix look like this: $\displaystyle \alpha(x) x+\beta(x) \mathrm{e}^{x}=0 \\ \alpha(x) +\beta(x) \mathrm{e}^{x} =(x-1)^2$ or this: $\displaystyle \alpha(x) x+\beta(x)\mathrm{e}^{x}=0 \\ \alpha(x) +\beta(x) \mathrm{e}^{x} =(x-1)$ ? Any help would be appreciated.

 Tags 2nd, differential, equation, order, parameters, variation

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