solve : x^2y"-3xy'+3y=x+x^2
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give the question clearly
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x2y"−3xy′+3y=2x4ex
This is an Euler-Cauchy differential equation. Find the characteristic polynomial given y=xr to solve the homogenous equation.
Let y=xr,y′=rxr−1,y′=r(r−1)xr−2 .
x2y"−3xy′+3y=0
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