Solve these ODEs. Solve the IVP if an initial condition is given, otherwise, find the general

solution. If your solution cannot be expressed analytically, i$.$e$.$ using the functions sin$,$ cos$,$ exp,

polynomials, and the inverses of these functions, then you should express your solution either

implicitly, or using an integral, whichever is appropriate.

$($a$)$ dy

dt $=$y $+$ t$2,$ y$(0)=1$

$($b$)$ dy

dx sin y $=$ cos y

$(1+$e$$x $)$

$($c$)$ dy

dx $+$ y cot x $=5$ecos x

$($d$)1+$ x$2$ dy

dx $+2$xy $=$ cot x

$($e$)$ x dy

dx $=$ y ln y

$($f$)$ dy

dt $=$ y$2$

$13$ty $,$ y$(1)=2$

$($Hint: Consider y as the independent variable and t as the dependent variable