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Question

Show that y = ae2x + be−x is a solution of the differential equation d2ydx2-dydx-2y=0.

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Solution

We have,
y=ae2x+be-x ...(1)
Differentiating both sides of equation (1) with respect to x, we get
dydx=2ae2x-be-x ...(2)
Differentiating both sides of equation (2) with respect to x, we get
d2ydx2=4ae2x+be-xd2ydx2=2ae2x-be-x+2ae2x+2be-xd2ydx2=2ae2x-be-x+2ae2x+be-xd2ydx2=dydx+2y Using equations 1 and 2
d2ydx2-dydx-2y=0
Hence, the given function is the solution to the given differential equation.

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