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The solution of the differential equatio...

The solution of the differential equation `((x+2y^3)dy)/(dx)=y` is

A

`x/y^(2)=y+c`

B

`x/y=y^(2)+c`

C

`x^(2)/y=y^(2)+c`

D

`y/x=x^(2)+c`

Text Solution

Verified by Experts

The correct Answer is:
B
`(dy)/(dx) = (x+2y^(3))/(y)`
or `(dx)/(dy)-1/yx=2y^(2)` which is linear
I.F. `e^(int-1/ydy)=e^(-logy) = 1/y`
Thus, solution is `1/yx = int1/y2y^(2)dy+c=y^(2)+c`
or `x/y=y^(2)+c`
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