Internal problem ID [11034]
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 4(c).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-2 x \left (t \right )-2 y \left (t \right )+4 z \left (t \right )\\ y^{\prime }\left (t \right )&=-2 x \left (t \right )+y \left (t \right )+2 z \left (t \right )\\ z^{\prime }\left (t \right )&=-4 x \left (t \right )-2 y \left (t \right )+6 z \left (t \right )+{\mathrm e}^{2 t} \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 89
dsolve([diff(x(t),t)=-2*x(t)-2*y(t)+4*z(t),diff(y(t),t)=-2*x(t)+1*y(t)+2*z(t),diff(z(t),t)=-4*x(t)-2*y(t)+6*z(t)+exp(2*t)],[x(t), y(t), z(t)], singsol=all)
\[ x \left (t \right ) = \frac {3 c_{2} {\mathrm e}^{2 t}}{4}+4 \,{\mathrm e}^{2 t} t -\frac {19 \,{\mathrm e}^{2 t}}{4}+{\mathrm e}^{t} c_{3} -\frac {{\mathrm e}^{2 t} c_{1}}{2} \] \[ y \left (t \right ) = \frac {c_{2} {\mathrm e}^{2 t}}{2}+2 \,{\mathrm e}^{2 t} t -\frac {5 \,{\mathrm e}^{2 t}}{2}+\frac {{\mathrm e}^{t} c_{3}}{2}+{\mathrm e}^{2 t} c_{1} \] \[ z \left (t \right ) = \left ({\mathrm e}^{t} \left (5 t +c_{2} -5\right )+c_{3} \right ) {\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 119
DSolve[{x'[t]==-2*x[t]-2*y[t]+4*z[t],y'[t]==-2*x[t]+y[t]+2*z[t],z'[t]==-4*x[t]-2*y[t]+6*z[t]+Exp[2*t]},{x[t],y[t],z[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^t \left (e^t (4 t-4-3 c_1-2 c_2+4 c_3)+2 (2 c_1+c_2-2 c_3)\right ) \\ y(t)\to e^t \left (2 e^t (t-1-c_1+c_3)+2 c_1+c_2-2 c_3\right ) \\ z(t)\to e^t \left (e^t (5 t-2 (2+2 c_1+c_2)+5 c_3)+2 (2 c_1+c_2-2 c_3)\right ) \\ \end{align*}