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Question

If d2xdy2(dydx)3+d2ydx2=K then the value of K is equal to

A
1
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B
1
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C
2
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D
0
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Solution

The correct option is D 0
Let y=f(x)
So, dydx=f(x)

dxdy=1f(x)

d2xdy2=f′′(x).dxdy(f(x))2=f′′(x).1f(x)(f(x))2
and
d2ydx2=f′′(x)

So, d2xdy2(dydx)3+d2ydx2

=f′′(x)(f(x))3.(f(x))3+f′′(x)=0=K

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