Internal problem ID [1867]
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: 16.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )+{\mathrm e}^{2 t}\\ x_{2}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )+3 x_{2} \left (t \right )-4 x_{3} \left (t \right )+2 \,{\mathrm e}^{2 t}\\ x_{3}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )+x_{2} \left (t \right )-4 x_{3} \left (t \right )+{\mathrm e}^{2 t} \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 84
dsolve([diff(x__1(t),t)=1*x__1(t)+1*x__2(t)-1*x__3(t)+exp(2*t),diff(x__2(t),t)=2*x__1(t)+3*x__2(t)-4*x__3(t)+2*exp(2*t),diff(x__3(t),t)=4*x__1(t)+1*x__2(t)-4*x__3(t)+exp(2*t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= {\mathrm e}^{2 t} t +c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{-3 t}+c_{3} {\mathrm e}^{2 t} \\ x_{2} \left (t \right ) &= 2 \,{\mathrm e}^{2 t} t +c_{1} {\mathrm e}^{t}+7 c_{2} {\mathrm e}^{-3 t}+2 c_{3} {\mathrm e}^{2 t} \\ x_{3} \left (t \right ) &= {\mathrm e}^{2 t} t +c_{1} {\mathrm e}^{t}+11 c_{2} {\mathrm e}^{-3 t}+c_{3} {\mathrm e}^{2 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.128 (sec). Leaf size: 2491
DSolve[{x1'[t]==1*x1[t]+1*x2[t]-1*x3[t]+Exp[2*t],x2'[t]==2*x1[t]+3*x2[t]-4*x3[t]+2*Exp[2*t],x3'[t]==4*x1[t]-1*x2[t]-4*x3[t]+Exp[2*t]},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
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