Internal problem ID [784]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 7.9, Nonhomogeneous Linear Systems. page 447
Problem number: 7.
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 )+2 \,{\mathrm e}^{t}\\ x_{2}^{\prime }\left (t \right )&=4 x_{1} \left (t \right )+x_{2} \left (t \right )-{\mathrm e}^{t} \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 44
dsolve([diff(x__1(t),t)=1*x__1(t)+1*x__2(t)+2*exp(t),diff(x__2(t),t)=4*x__1(t)+1*x__2(t)-exp(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= c_{2} {\mathrm e}^{3 t}+{\mathrm e}^{-t} c_{1} +\frac {{\mathrm e}^{t}}{4} \\ x_{2} \left (t \right ) &= 2 c_{2} {\mathrm e}^{3 t}-2 \,{\mathrm e}^{-t} c_{1} -2 \,{\mathrm e}^{t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 80
DSolve[{x1'[t]==1*x1[t]+1*x2[t]+2*Exp[t],x2'[t]==4*x1[t]+1*x2[t]-Exp[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{4} e^{-t} \left (e^{2 t}+(2 c_1+c_2) e^{4 t}+2 c_1-c_2\right ) \\ \text {x2}(t)\to \frac {1}{2} e^{-t} \left (-4 e^{2 t}+(2 c_1+c_2) e^{4 t}-2 c_1+c_2\right ) \\ \end{align*}