Internal problem ID [781]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 7.9, Nonhomogeneous Linear Systems. page 447
Problem number: 4.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=x_{1} \relax (t )+x_{2} \relax (t )+{\mathrm e}^{-2 t}\\ x_{2}^{\prime }\relax (t )&=4 x_{1} \relax (t )-2 x_{2} \relax (t )-2 \,{\mathrm e}^{t} \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 45
dsolve([diff(x__1(t),t)=1*x__1(t)+1*x__2(t)+exp(-2*t),diff(x__2(t),t)=4*x__1(t)-2*x__2(t)-2*exp(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \relax (t ) = c_{2} {\mathrm e}^{2 t}-\frac {c_{1} {\mathrm e}^{-3 t}}{4}+\frac {{\mathrm e}^{t}}{2} \] \[ x_{2} \relax (t ) = c_{2} {\mathrm e}^{2 t}+c_{1} {\mathrm e}^{-3 t}-{\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.586 (sec). Leaf size: 84
DSolve[{x1'[t]==1*x1[t]+1*x2[t]+Exp[-2*t],x2'[t]==4*x1[t]-2*x2[t]-2*Exp[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {e^t}{2}+\frac {1}{5} (c_1-c_2) e^{-3 t}+\frac {1}{5} (4 c_1+c_2) e^{2 t} \\ \text {x2}(t)\to \frac {1}{5} e^{-3 t} \left (-5 e^t+(4 c_1+c_2) e^{5 t}-4 c_1+4 c_2\right ) \\ \end{align*}