$In$ Problems $1-22$ solve the given differential equation $by$

separation $of$ variables.

$\frac{dy}{dx}=sin5x$

$\frac{dy}{dx}=(x+1{)}^2$

$dx+e^{3x}dy=0$

$dy-(y-1{)}^{2}dx=0$

$x\frac{dy}{dx}=4y$

$\frac{dy}{dx}+2x{y}^2=0$

$\frac{dy}{dx}=e^{3x+2y}$

$e^{x}y\frac{dy}{dx}=e^{-y}+e^{-2x-y}$

$ylnx\frac{dx}{dy}=(\frac{y+1}{x}{)}^2$

$\frac{dy}{dx}=(\frac{2y+3}{4x+5}{)}^2$

$cscydx+se{c}^{2}xdy=0$

$sin3xdx+2yco{s}^{3}3xdy=0.$

$(e^y+1{)}^2{e}^{-y}dx+(e^x+1{)}^3{e}^{-x}dy=0$

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

$\frac{dS}{dr}=kS$

$\frac{dQ}{dt}=k(Q-70)$

$\frac{dP}{dt}=P-P^2$

$\frac{dN}{dt}+N=N{c}^{t+2}$