Question

Solve the differential equation:
$(x+1)dy-2xydx=0$

Answer 1

$(x+1)dy-2xydx=0$

$\frac{dy}{dx}=\frac{2xy}{x+1}$

$\frac{1}{y}dy=\left(\frac{2x}{x+1}\right)dx$

$\frac{1}{y}dy=[\frac{2(x+1)}{(x+1)}=\frac{2}{(x+1)}]dx$

$\int \frac{1}{y}dy=\int 2dx-\int \frac{2}{(x+1)}dx$

$\log |y|=2x-2\log |x+1|+\log c$

$\log |y|+2\log |x+1|-\log c=2x$

$\frac{\log y(x+1{)}^2}{c}=2x$

$\frac{y(x+1{)}^2}{c}=c^{2x}$

$y=\frac{c{e}^{2x}}{(x+1{)}^2}$