Use reduction of order to find a second solution to the given differential equation(adsbygoogle = window.adsbygoogle || []).push({});

(x-1)y"-xy'+y=0 x>1 y_1=e^x

Putting it in standard form gives

[tex] y"-x/x-1 y' + 1/x-1 y =0 [/tex]

y(t)=v(t)e^x

y'(t)= v'(t)e^x +v(t)e^x

y"(t)= v"(t)+2v'(t)e^x +v(t)e^x

plugging into the initial equation:

[tex] v"(t)e^x+2v'(t)e^x+v(t)e^x-xv'(t)e^x/x-1 +xv(t)e^x/x-1 +v(t)e^x/x-1 [/tex]

I'm not sure how to simplify this further if it can even be done, or what I should do next. Can someone please help me out?

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# Homework Help: 2nd order ODE

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