In Exercises $25-38,$ solve the given initial$-$value problem.

$(25)\frac{dx}{dt}=-xt,$

$x(0)=\frac{1}{\sqrt[\phantom{2}]{}}$

$26.\frac{dy}{dt}=ty,y(0)=3$

$(27.)\frac{dy}{dt}=-y^2,y(0)=\frac{1}{2}$

$28.\frac{dy}{dt}=t^2{y}^3,y(0)=-1$

$29.\frac{dy}{dt}=-y^2,y(0)=0$

$30.\frac{dy}{dt}=\frac{t}{y-t^{2}y},y(0)=4$

$(31.)\frac{dy}{dt}=2y1,y(0)=3$

$32.\frac{dy}{dt}=t{y}^{2}2y^2,y(0)=1$

$33.\frac{dx}{dt}=\frac{t^2}{x{t}^{3}x},x(0)=-2$

$34.\frac{dy}{dt}=\frac{1-y^2}{y},y(0)=-2$

$(35.)\frac{dy}{dt}=(y^{2}1)t,y(0)=1$

$36.\frac{dy}{dt}=\frac{1}{2y3},y(0)=1$

$(37.)\frac{dy}{dt}=2t{y}^{2}3t^2{y}^2,$

$y(1)=-1$

$38.\frac{dy}{dt}=\frac{y^{2}5}{y},y(0)=-2$