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Question

Verify that y=2sin3x is the solution of the D.E d2ydx2+9y=0

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Solution

y=2sin3x

dydx=6cos3x

d2ydx2=18sin3x

d2ydx2+9y=18sin3x+9(2sin3x)
=18sin3x+18sin3x
=0

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