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If y=f(x) is solution of differentiable ...

If `y=f(x)` is solution of differentiable equation `(dy)/(dx)=y/x((1-3x^(2)y^(3)))/((2x^(2)y^(3)+1))`, then (`f(x).x)^(3)` is equal to

A

`x+cy`

B

`2x+cy`

C

`x^(2)+cy`

D

`x^(3)+cy^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`x(2x^(2)y^(3)+1)dy=y(1-3x^(2)y^(3))dx`
`impliesx^(2)(2xdy+3ydx)=(ydx-xdy)/(y^(2))`
`impliesd(x^(3)y^(2))= x/y +c`
`impliesx^(3)y^(3)=x+cy`
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