Solve these ODEs. Solve the IVP if an initial condition is given, otherwise, find the generalsolution. 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 eitherimplicitly, or using an integral, whichever is appropriate.$($a$)$ dydt $=$ y $+$ t$2,$ y$(0)=1($b$)$ dydx sin y $=$ cos y$(1+$ex$)($c$)$ dydx $+$ y cot x $=5$ecos x$($d$)1+$ x$2$ dydx $+2$xy $=$ cot x$($e$)$ x dydx $=$ y ln y$($f$)$ dydt $=$ y$213$ty $,$ y$(1)=2($Hint: Consider y as the independent variable and t as the dependent variable.