Internal problem ID [778]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 7.9, Nonhomogeneous Linear Systems. page 447
Problem number: 1.
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 )+t \end {align*}
✓ Solution by Maple
Time used: 0.042 (sec). Leaf size: 54
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)+t],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = \frac {c_{2} {\mathrm e}^{-t}}{3}+c_{1} {\mathrm e}^{t}+\frac {3 t \,{\mathrm e}^{t}}{2}-\frac {{\mathrm e}^{t}}{4}+t \] \[ x_{2}\relax (t ) = c_{2} {\mathrm e}^{-t}+c_{1} {\mathrm e}^{t}+\frac {3 t \,{\mathrm e}^{t}}{2}-\frac {3 \,{\mathrm e}^{t}}{4}+2 t -1 \]
✓ Solution by Mathematica
Time used: 0.116 (sec). Leaf size: 86
DSolve[{x1'[t]==2*x1[t]-1*x2[t]+Exp[t],x2'[t]==3*x1[t]-2*x2[t]+t},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to t+\frac {1}{4} e^t (6 t-1+6 c_1-2 c_2)+\frac {1}{2} (c_2-c_1) e^{-t} \\ \text {x2}(t)\to \frac {1}{4} \left (8 t+e^t (6 t-3+6 c_1-2 c_2)-6 (c_1-c_2) e^{-t}-4\right ) \\ \end{align*}