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If y=e^(-x)(A cos x + B sin x) then y is...

If `y=e^(-x)(A cos x + B sin x)` then y is a solution of

A

`(d^(2)y)/(dx^(2))+2(dy)/(dx)=0`

B

`(d^(2)y)/(dx^(2))-2(dy)/(dx)+2y=0`

C

`(d^(2)y)/(dx^(2))+2(dy)/(dx)+2y=0`

D

`(d^(2)y)/(dx^(2))+2y=0`

Text Solution

AI Generated Solution

To find the differential equation for which \( y = e^{-x}(A \cos x + B \sin x) \) is a solution, we will differentiate \( y \) twice and eliminate the constants \( A \) and \( B \). ### Step 1: Differentiate \( y \) with respect to \( x \) Given: \[ y = e^{-x}(A \cos x + B \sin x) \] ...
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