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Question

The solution of y=x(dydx)+(dydx)3 are given by (where p=dy/dx and k is constant).

A
y=0
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B
y=kx+k3
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C
y=kex+k
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D
None of these
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Solution

The correct option is A y=0

Put p=dydx in the given equation y=x(dydx)+(dydx)3.

y=px+p3

dydx=dpdx(x)+p+3p2dpdx

p=xdpdx+p+3p2dpdx

dpdx(x+3p2)=0

dpdx=0;x+3p2=0

p=0;p2=x3

dydx=0

y=0


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