Question

Differential equations

Answer 1

I have:
\[(2x^{2} + y) dx + (x^{2} y - x) dy = 0 \]

Answer 2

did you get it @sirm3d ??

Answer 3

\[\large 2x^2dx+ydx+x^2ydy-xdy=0\]\[\large 2x^2dx-(xdy-ydx)+x^2ydy=0\]divide everything by x^2
\[\large2dx-\frac{ xdy-ydx }{ x^2 }+ydy=0\]thesecond term is the differential d(y/x)\[\large2dx-d\left(\frac{y}{x}\right)+ydy=0\]integrate\[\large 2x-\frac{ y }{ x }+\frac{ y^2 }{ 2 }=\frac{ C }{ 2 }\]\[\large 4x^2-2y+2xy^2=Cx\]

Answer 4

I got

\[2x + \frac{ 1 }{ 2 } y^{2} -\frac{ y }{ x } = C\]

Answer 5

that is also correct. the difference in our answer is the choice of the constant.

Answer 6

very nice..., Thank You for Checking :)