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 }\relax (t )&=x_{1} \relax (t )+x_{2} \relax (t )-x_{3} \relax (t )+{\mathrm e}^{2 t}\\ x_{2}^{\prime }\relax (t )&=2 x_{1} \relax (t )+3 x_{2} \relax (t )-4 x_{3} \relax (t )+2 \,{\mathrm e}^{2 t}\\ x_{3}^{\prime }\relax (t )&=4 x_{1} \relax (t )+x_{2} \relax (t )-4 x_{3} \relax (t )+{\mathrm e}^{2 t} \end {align*}
✓ Solution by Maple
Time used: 0.203 (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)],[x__1(t), x__2(t), x__3(t)], singsol=all)
\[ x_{1} \relax (t ) = {\mathrm e}^{2 t} t +c_{1} {\mathrm e}^{t}+\frac {c_{2} {\mathrm e}^{-3 t}}{11}+c_{3} {\mathrm e}^{2 t} \] \[ x_{2} \relax (t ) = 2 \,{\mathrm e}^{2 t} t +c_{1} {\mathrm e}^{t}+\frac {7 c_{2} {\mathrm e}^{-3 t}}{11}+2 c_{3} {\mathrm e}^{2 t} \] \[ x_{3} \relax (t ) = {\mathrm e}^{2 t} t +c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{-3 t}+c_{3} {\mathrm e}^{2 t} \]
✓ Solution by Mathematica
Time used: 0.121 (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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