Internal problem ID [785]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 7.9, Nonhomogeneous Linear Systems. page 447
Problem number: 8.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=2 x_{1} \relax (t )-x_{2} \relax (t )+{\mathrm e}^{t}\\ x_{2}^{\prime }\relax (t )&=3 x_{1} \relax (t )-2 x_{2} \relax (t )-{\mathrm e}^{t} \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 43
dsolve([diff(x__1(t),t)=2*x__1(t)-1*x__2(t)+exp(t),diff(x__2(t),t)=3*x__1(t)-2*x__2(t)-exp(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \relax (t ) = \frac {c_{2} {\mathrm e}^{-t}}{3}+c_{1} {\mathrm e}^{t}+{\mathrm e}^{t}+2 t \,{\mathrm e}^{t} \] \[ x_{2} \relax (t ) = c_{2} {\mathrm e}^{-t}+c_{1} {\mathrm e}^{t}+2 t \,{\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 80
DSolve[{x1'[t]==2*x1[t]-1*x2[t]+Exp[t],x2'[t]==3*x1[t]-2*x2[t]-Exp[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{2} e^{-t} \left (e^{2 t} (4 t-1+3 c_1-c_2)-c_1+c_2\right ) \\ \text {x2}(t)\to \frac {1}{2} e^{-t} \left (e^{2 t} (4 t-3+3 c_1-c_2)-3 c_1+3 c_2\right ) \\ \end{align*}