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Question

If y2=p(x) is a polynomial of degree 3, then 2ddx [y3d2ydx2] is equal to

A
p"' (x) + p' x
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B
p''(x). p"'(x)
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C
p (x). p"' (x)
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D
None of these
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Solution

The correct option is C p (x). p"' (x)
y2=P(x)2yy=p(x)-----(i)
(2y)y′′+y(2y)=p′′(x)
2yy′′=p′′(x)2(y)2
2y3y′′=y2p′′(x)2(yy)2
2y3y′′=y2p′′(x)2(p(x)2)4[from Eq.(i)]
2y3y′′=p(x)p′′(x)12p(x)2
ddx(2y3y′′)=p(x)p′′′(x)+p(x)p′′(x)p(x)p′′(x)=p(x).p′′′(x)
2ddx(y3d2ydx2)=p(x)p′′′(x)

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