Find the general solution of the differential equation `y dx-(x+2y^2)dy=0`.

Options

A. `x=y^(2)+cy`
B. `x = 2cy^(2)`
C. ` x = 2y^(2)+cy `
D. none of the above

Answer

C

Explanation

` ydx-xdy -2y^(2) dy =0`
` Rightarrow ydx -xdy - 2y^(2)dy =0`
` Rihgtarrow y-x .(dy)/(dx) =2y^(2) .(dy)/(dx)`
` Rightarrow ( y-x.(dy)/(dx))/(y^(2)) =2.(dy)/(dx)`
Integrating
` Rightarrow x/y =2 y+c`
` Rightarrow x = 2y^(2) +cy`