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Question

Show that y = bex + ce2x is a solution of the differential equation, d2ydx2-3dydx+2y=0.

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Solution

We have,
y=bex+ce2x ...(1)
Differentiating both sides of equation (1) with respect to x, we get
dydx=bex+2ce2x ...(2)
Differentiating both sides of equation (2) with respect to x, we get
d2ydx2=bex+4ce2x= 3bex+6ce2x-2bex-2ce2x= 3bex+2ce2x-2bex+ce2x= 3dydx-2y Using equations 1 and 2
d2ydx2-3dydx+2y=0
Hence, the given function is the solution to the given differential equation.

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