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Question

The solution of the differential equation d2ydx2+dydx+y=0 is

A
Aex+Bex
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B
ex(Ax+B)
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C
ex{Acos(32)x+Bcos(32)x}
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D
ex2{Acos(32)x+Bsin(32)x}
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Solution

The correct option is D ex2{Acos(32)x+Bsin(32)x}
d2ydx2+dydx+y=0

D2+D+1=0

D=1±3i2

y=ex/2[Acos32x+Bsin32x]

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