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: 0.062 (sec). Leaf size: 83
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)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \left (t \right ) = \frac {\sqrt {7}\, {\mathrm e}^{\sqrt {7}\, t} c_{2}}{3}-\frac {\sqrt {7}\, {\mathrm e}^{-\sqrt {7}\, t} c_{1}}{3}+3 \,{\mathrm e}^{3 t}+\frac {2 \,{\mathrm e}^{\sqrt {7}\, t} c_{2}}{3}+\frac {2 \,{\mathrm e}^{-\sqrt {7}\, t} c_{1}}{3} \] \[ x_{2} \left (t \right ) = {\mathrm e}^{\sqrt {7}\, t} c_{2} +{\mathrm e}^{-\sqrt {7}\, t} c_{1} +2 \,{\mathrm e}^{3 t} \]
✓ Solution by Mathematica
Time used: 0.378 (sec). Leaf size: 100
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 3 \sinh (3 t)+3 \cosh (3 t)+c_1 \cosh \left (\sqrt {7} t\right )+\frac {(2 c_1+c_2) \sinh \left (\sqrt {7} t\right )}{\sqrt {7}} \\ \text {x2}(t)\to 2 \sinh (3 t)+2 \cosh (3 t)+c_2 \cosh \left (\sqrt {7} t\right )+\frac {(3 c_1-2 c_2) \sinh \left (\sqrt {7} t\right )}{\sqrt {7}} \\ \end{align*}