$In$ each $of$ Problems $5$ through $10,$ verify that each given function $isa$

solution $of$ the differential equation.

$y^{\text{'}\text{'}}-y=0$;$,y_1(t)=e^t,y_2(t)=cosh(t)$

$y^{\text{'}\text{'}}+2y^{\text{'}}-3y=0$;$,y_1(t)=e^{-3t},y_2(t)=e^t$

$t{y}^{\text{'}}-y=t^2$;$,y=3t+t^2$

$y^{\text{'}\text{'}\text{'}\text{'}}+4y^{\text{'}\text{'}\text{'}}+3y=t$;$,y_1(t)=\frac{t}{3},y_2(t)=e^{-t}+\frac{t}{3}$

$t^2{y}^{\text{'}\text{'}}+5t{y}^{\text{'}}+4y=0,t>0$;$,y_1(t)=t^{-2},y_2(t)=t^{-2}ln(t)$

$y^{\text{'}}-2ty=1$;$,y=e^{t^2}{\displaystyle \underset{0}{\overset{t}{}}}{e}^{-s^2}ds+e^{t^2}$