Internal problem ID [1862]
Book: Differential equations and their applications, 4th ed., M. Braun
Section: Section 3.12, Systems of differential equations. The nonhomogeneous equation. variation
of parameters. Page 366
Problem number: 10.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+x_{2} \left (t \right )+{\mathrm e}^{3 t}\\ x_{2}^{\prime }\left (t \right )&=3 x_{1} \left (t \right )-2 x_{2} \left (t \right )+{\mathrm e}^{3 t} \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 82
dsolve([diff(x__1(t),t)=2*x__1(t)+1*x__2(t)+1*exp(3*t),diff(x__2(t),t)=3*x__1(t)-2*x__2(t)+exp(3*t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{\sqrt {7}\, t} c_{2} +{\mathrm e}^{-\sqrt {7}\, t} c_{1} +3 \,{\mathrm e}^{3 t} \\ x_{2} \left (t \right ) &= \sqrt {7}\, {\mathrm e}^{\sqrt {7}\, t} c_{2} -\sqrt {7}\, {\mathrm e}^{-\sqrt {7}\, t} c_{1} +2 \,{\mathrm e}^{3 t}-2 \,{\mathrm e}^{\sqrt {7}\, t} c_{2} -2 \,{\mathrm e}^{-\sqrt {7}\, t} c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.411 (sec). Leaf size: 171
DSolve[{x1'[t]==2*x1[t]+1*x2[t]+Exp[3*t],x2'[t]==3*x1[t]-2*x2[t]+Exp[3*t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{14} e^{-\sqrt {7} t} \left (42 e^{\left (3+\sqrt {7}\right ) t}+\left (\left (7+2 \sqrt {7}\right ) c_1+\sqrt {7} c_2\right ) e^{2 \sqrt {7} t}+\left (7-2 \sqrt {7}\right ) c_1-\sqrt {7} c_2\right ) \\ \text {x2}(t)\to \frac {1}{14} e^{-\sqrt {7} t} \left (28 e^{\left (3+\sqrt {7}\right ) t}+\left (3 \sqrt {7} c_1+\left (7-2 \sqrt {7}\right ) c_2\right ) e^{2 \sqrt {7} t}-3 \sqrt {7} c_1+\left (7+2 \sqrt {7}\right ) c_2\right ) \\ \end{align*}