$In$ Problems $24$ find the general solution $of$ the given differential

equation. Give the largest interval I over which the

general solution $is$ defined. Determine whether there are any

transient terms $in$ the general solution.

$24.$

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

$In$ Problems $25-30$ solve the given initial$-$value problem.

Give the largest interval I over which the solution $is$ defined.

$25.$

$x{y}^{\text{'}}+y=e^x,y(1)=2$

$26.$

$y\frac{dx}{dy}-x=2y^2,y(1)=5$

$27.$

$L\frac{di}{dt}+Ri-E,i(0)=i_0$

$L,R,E,$ and $i_0$ constants

$28.$

$\frac{dT}{dt}=k(T-T_m)$;$,T(0)=T_0$

$k,T_m,$ and $T_0$ constants

$29.$

$(x+1)\frac{dy}{dx}+y=lnx,y(1)=10$

$30.$

$y^{\text{'}}+(tanx)y=co{s}^{2}x,y(0)=-1$