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Question

If x=sint,y=sinkt, then (1−x2)y2−xy1=

A
ky
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B
ky
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C
k2y
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D
k2y
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Solution

The correct option is C k2y

dydx=dydtdxdt=kcos ktcos t
d2ydx2=ddt(dydx)dtdx=k(ksin k.tcos t+sin t.cos ktcos2t)1cos t
y2cos2t=k2sinkt+sintcosktcost(k)
(1x2)y2=k2y+xy1
(1x2)y2xy1=k2y


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