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Differential Equations

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Moderate

Identifying All Particular Solutions

DIFFEQ-QL0JHC

Consider the equation:

$$xy''-(1+x)y'+y=2x^2e^{2x}$$

Two solutions of the corresponding homogeneous equation are $y_1(x)=1+x$ and $y_2(x)=e^x$.

Which of the following are particular solutions?

Select ALL that apply.

A

$(x-1)e^{2x}$

B

$(x-1)e^{2x}+e^x-1-x$

C

$(x^2-\frac{5}{2}x+\frac{5}{2})e^{2x}$

D

$x^2e^{2x}-\frac{5}{2}xe^{2x}+\frac{5}{2}e^{2x}-e^x$