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Verify that y = e^(-2x) is a solution of...

Verify that `y = e^(-2x)` is a solution of the differential equation `y'' + 4y'' - 3y' - 2y = 0`.

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`y = e^(-2x)`
`rArr y' = -2e^(-2x)`
`rArr y' = 4e^(-2x)`
`y'' = -8e^(-2x)`
Substituting these derivatives in given differential equation we get
`L.H.S. = y'' + y'' - 3y' - 2y`
`= -8e^(-2x) + 4(4e^(2x)) - 3(-2e^(-2x)) - 2e^(-2x)`
0
= RHS
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