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Solution of the differential y' = (3yx^(...

Solution of the differential y' = `(3yx^(2))/(x^(3)+2y^(4))` is

A

`x^(3)y^(-1)=(2)/(3)y^(3)+c`

B

`x^(2)y^(-1)=(2)/(3)y^(3)+c`

C

`xy^(-1)=(2)/(3)y^(3)+c`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`(3yx^(2))dx - x^(3)dy = 2y^(4)dy`
`rArr" "yd(x^(3))-x^(3)dy = 2y^(4)dy`
`rArr" "(yd(x^(3))-x^(3)dy)/(y^(2))=2y^(2)dy`
`rArr" "d((x^(3))/(y))=2y^(2)dy`
`rArr" "(x^(3))/(y)=(2)/(3)y^(3)+c`
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