Maths Solve the Following Question.(5 Marks)

y + 1) = c(1 – x – y – 2xy).

$2 e^{\frac{x}{y}} d x+\left(y-2 x e^{\frac{x}{y}}\right) d y=0$, when $y(0)=1$

$\frac{d y}{d x}-3 y \cot x =\sin 2 x$, when $y \left(\frac{\pi}{2}\right)=2$

$y(1+\log x)=(\log x x) \frac{d y}{d x}$, when $y(e)= e ^2$

$y \log y=\left(\log y^2-x\right) \frac{d y}{d x}$

$\frac{d y}{d x}=\frac{2 y-x}{2 y+x}$

$\left(x^2+y^2\right) d x-2 x y d y=0$

$\frac{d y}{d x}+\frac{x-2 y}{2 x-y}=0$

$\left(x^2-y^2\right) d x+2 x y d y=0$

$y^2 d x+\left(x y+x^2\right) d y=0$