In Prodismi $7-16,$ solve the equation.

$7.x\frac{dy}{dx}=\frac{1}{y^3}$

$8.\frac{dx}{dt}=3x{t}^2$

$9.\frac{dx}{dt}=\frac{t}{x{e}^{t+2x}}$

$10.\frac{dy}{dx}=\frac{x}{y^2\sqrt[\phantom{2}]{1+x}}$

$11.x\frac{dv}{dx}=\frac{1-4v^2}{3v}$

$12.\frac{dy}{dx}=\frac{se{c}^{2}y}{1+x^2}$

$13.\frac{dy}{dx}=3x^2(1+y^2{)}^{\frac{3}{2}}$

$14.\frac{dx}{dt}-x^3=x$

$15.(x+x{y}^2)dx+e^{x^2}ydy=0$

$16.y^{-1}dy+y{e}^{cosx}sinxdx=0$

Only need help on $13$ and $15$ please as I was really struggling to solve those two. Solve the differential equations please show steps explaining.