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Differential Equations

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Moderate

Variation of Parameters for a Particular Solution

DIFFEQ-OC2GNE

Consider:

$$y''-2y'+y=e^x/(1+x^2)$$

We can use the variation of parameters to find a particular solution. Which of the following are particular solutions? Select the best answer.

A

$-\cfrac{1}{2}\ln(x^2+1)e^x+xe^x\arctan(x)$

B

$2e^x-\cfrac{1}{2}\ln(x^2+1)e^x+xe^x\arctan(x)$

C

$3xe^x-\cfrac{1}{2}\ln(x^2+1)e^x+xe^x\arctan(x)$

D

$4e^x-xe^x-\cfrac{1}{2}\ln(x^2+1)e^x+xe^x\arctan(x)$

E

All of the above.