Internal problem ID [12388]
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).
ODE order: 1.
ODE degree: 1.
Solve \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 \[ [x \left (0\right ) = 1, y \left (0\right ) = 2, z \left (0\right ) = 3] \]
✓ Solution by Maple
Time used: 5.609 (sec). Leaf size: 949416
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: 0.228 (sec). Leaf size: 3462
DSolve[{x'[t]==-3*x[t]-3*y[t]+z[t],y'[t]==2*y[t]+2*z[t]+29*Exp[-t],z'[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