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Question

If d2ydt2+y=0 under the conditions y=1,dydt=0, when t=0 then y is equal to

A
sint
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B
cost
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C
tant
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D
cott
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Solution

The correct option is B cost
d2ydt2+y=0(D2+1)y=0 ...(i)
Wherer D=ddt
AE is m2+1=0m=±i
So CF=eot(C1cost+C2sint] and PI=0
Hence General solutin is y=CF+PI
y=C1cost+C2sint .... (ii)
dydx=C1sint+C2cost ....(iii)
Using y(0)=11=C1+0C1=1
Using y(0)=00=0+C2C2=0
So y=cost

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