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May 8th, 2014, 11:26 AM  #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 (x1)y''xy'+y=(x1)^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 (x1) first? I.E. will the system of equations with the fundamental matrix look like this: $\displaystyle \alpha(x) x+\beta(x) \mathrm{e}^{x}=0 \\ \alpha(x) +\beta(x) \mathrm{e}^{x} =(x1)^2$ or this: $\displaystyle \alpha(x) x+\beta(x)\mathrm{e}^{x}=0 \\ \alpha(x) +\beta(x) \mathrm{e}^{x} =(x1)$ ? Any help would be appreciated. 

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