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 }\relax (t )&=x_{1} \relax (t )+x_{2} \relax (t )+2 \,{\mathrm e}^{t}\\ x_{2}^{\prime }\relax (t )&=4 x_{1} \relax (t )+x_{2} \relax (t )-{\mathrm e}^{t} \end {align*}
✓ Solution by Maple
Time used: 0.063 (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)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \relax (t ) = \frac {c_{2} {\mathrm e}^{3 t}}{2}-\frac {{\mathrm e}^{-t} c_{1}}{2}+\frac {{\mathrm e}^{t}}{4} \] \[ x_{2} \relax (t ) = c_{2} {\mathrm e}^{3 t}+{\mathrm e}^{-t} c_{1}-2 \,{\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 54
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 (4 c_1 \cosh (2 t)+2 c_2 \sinh (2 t)+1) \\ \text {x2}(t)\to e^t (c_2 \cosh (2 t)+2 c_1 \sinh (2 t)-2) \\ \end{align*}