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Question

The differential equation of the family of the curves y=ex(Acosx+Bsinx), where A and B are arbitrary constants is

A
d2ydx2+(dydx)2+y=0
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B
d2ydx22dydx+2y=0
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C
d2ydx2+2dydx2y=0
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D
d2ydx22dydx+y=0
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Solution

The correct option is B d2ydx22dydx+2y=0
y=ex(Acosx+Bsinx) -------(i)
dydx=ex(Acosx+Bsinx)+ex(Asinx+Bcosx)
dydx=y+ex(Asinx+Bcosx) -------(ii)
Again differentiating both sides w.r.t. x, we get
d2ydx2=dydx+ex(Asinx+Bcosx)+ex(AcosxBsinx)
d2ydx2=dydx+dydxyy
d2ydx22dydx+2y=0

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