Solve the differential equation: `y\ dx+(x-y^2)dy=0`

Answer

`x=y^2/3+c/y`

Explanation

We have,


`y\ dx+(x-y^2)dy=0`


`y\ dx=(y^2-x)dy`


`rArr (dy)/(dx)=y/(y^2-x)`


`rArr (dx)/(dy)=(y^2-x)/y`


`rArr (dx)/(dy)=y-x/y`


`rArr (dx)/(dy)+x/y=y`


Comparing the equation with


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