Differential Equation Undetermined Coefficients: y'' - 2y' + y =xe^x

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Differential Equation Undetermined Coefficients: y'' - 2y' + y =xe^x
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Could help with this question:
For the following differential equation, find the general solution as a power series around x0 = 0, where y = y(x):
(1−𝑥) 𝑦" +2 𝑦′+𝑦=0

marciotardinmartins
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Please done this quation y''+y'-2y=xe^x

Saleamlak-tz
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how come yc = ce^x + cxe^x and not only yc = c1xe^x + c2xe^x?

edinaissa
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if i have y''-2y'+y= xe^(x)+3?

jordanzitzkepinhosd
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y ^^ - 2 y ^ + y = x e ^{x} + 4 please boss upload this question next videos.👍

abasadam
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isnt the last yp wrong ? it is said to multiply again with x^2

PedroSilva-gged