Solve this differential equation, and write the solution as a system of equations in x$,$ y$,$ and z$.$ The answer should NOT be in matrix form.

$$x$\text{'}=$x$+$y$+2$e$^5$t$4$ x$(0)=2$

y$\text{'}=$x$+2$y$+$z$+$e$^5$t$$y$(0)=1$

z$\text{'}=3$y$$z$3$e$^5$t$+6$z$(0)=1$