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Question

If y2 = ax2 + bx + c , then y3d2ydx2 is

A
a constant
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B
a function of x only
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C
a function of y only
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D
a function of x and y
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Solution

The correct option is D a function of x only
y2=ax2+bx+c
2ydydx=ddx(ax2)+ddx(bx)+ddx(c)
2ydydx=2ax+b+0
2ddx(ydydx)=ddx(2ax+b)
2(dydx)2+2yd2ydx2=2a
(dydx)2+yd2ydx2=a
yd2ydx2=a(dydx)2
yd2ydx2=a(2ax+b)2
y3d2ydx2=y2(a(2ax+b)2)
=(ax2+bx+c)(a4a2x2b24axb) is a function of x only


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