Solve the following differential equation $by$ using $an$ appropriate substitution

$i.x\frac{dy}{dx}+y=\frac{1}{y^2}$

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

iii. $t^2\frac{dy}{dt}+y^2=ty$

$iv.x\frac{dy}{dx}=y+\sqrt[\phantom{2}]{x^2-y^2},x>0$

$v.x^2\frac{dy}{dx}-2xy=3y^4,y(1)=\frac{1}{2}$

$vi.y^{\frac{1}{2}}\frac{dy}{dx}+y^{\frac{3}{2}}=1,y(0)=4$

vii. $x{y}^2\frac{dy}{dx}=y^3-x^3,y(1)=2$

viii. $ydx+x(lnx-lny-1)dy=0,y(1)=e$

$ix.(x+y{e}^{\frac{y}{x}})dx-x{e}^{\frac{y}{x}}dy=0,y(1)=0$