Suppose that $\displaystyle (x-1)y''-xy'+y=0$, and that x>1. Given that $\displaystyle y=e^x$ is a solution, use the reduction of order method to find a second solution.
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Reduction of order - Wikipedia, the free encyclopedia
Known solution
$\displaystyle
y_1=e^x
$
Find the solution of the form
$\displaystyle
y=y_1y_2
$