## Calculus (3rd Edition)

$$y=-6+11 e^{4t}$$
The general solution of $y'=4y+24=4(y+6)$ is $$y=-6+c e^{4t}.$$ When $y(0)=5$, then $5=-6+c$, i.e. $c=5+6=11$. Thus: $$y=-6+11 e^{4t}$$