67.7.13 problem Problem 6(a)

Internal problem ID [14124]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 8.3 Systems of Linear Differential Equations (Variation of Parameters). Problems page 514
Problem number : Problem 6(a)
Date solved : Tuesday, January 28, 2025 at 06:14:51 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )&=-3 x \left (t \right )-3 y+z \left (t \right )\\ y^{\prime }&=2 y+2 z \left (t \right )+29 \,{\mathrm e}^{-t}\\ z^{\prime }\left (t \right )&=5 x \left (t \right )+y+z \left (t \right )+39 \,{\mathrm e}^{t} \end{align*}

With initial conditions

\begin{align*} x \left (0\right ) = 1\\ y \left (0\right ) = 2\\ z \left (0\right ) = 3 \end{align*}

✓ Solution by Maple

Time used: 7.144 (sec). Leaf size: 949415

dsolve([diff(x(t),t) = -3*x(t)-3*y(t)+z(t), diff(y(t),t) = 2*y(t)+2*z(t)+29*exp(-t), diff(z(t),t) = 5*x(t)+y(t)+z(t)+39*exp(t), x(0) = 1, y(0) = 2, z(0) = 3], singsol=all)
 

\begin{align*} \text {Expression too large to display} \\ \text {Expression too large to display} \\ \text {Expression too large to display} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.088 (sec). Leaf size: 3462

DSolve[{D[x[t],t]==-3*x[t]-3*y[t]+z[t],D[y[t],t]==2*y[t]+2*z[t]+29*Exp[-t],D[z[t],t]==5*x[t]+y[t]+z[t]+39*Exp[t]},{x[0]==1,y[0]==2,z[0]==3},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
 

Too large to display