what is the solution of the differential equaiton
x dy-ydx =`xy^(2) dx` ?

Options

A. `yx^(2) +2x =2cy`
B. `y^(2)x+2y=2cx`
C. `y^(2)x^(2) +2x =2cy`
D. none of these

Answer

A

Explanation

Then , xdy - ydx = `xy^(2)dx` = xdx
` Rightarrow (xdy -ydx)/y^(2) = xdx Rightarrow (ydx -xdy)/y^(2) = -xdx`
` Rightarrow intd (x/y) =- intxdx Rightarrow x/y = (-x^(2))/2 + c = ( -x^(2) +2c)/2`
` Rightarrow yx^(2) +2x =2xy`