Internal problem ID [783]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 7.9, Nonhomogeneous Linear Systems. page 447
Problem number: 6.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=-\frac {4 x_{1}\relax (t ) t -2 x_{2}\relax (t ) t -1}{t}\\ x_{2}^{\prime }\relax (t )&=\frac {2 x_{1}\relax (t ) t -x_{2}\relax (t ) t +4 t +2}{t} \end {align*}
✓ Solution by Maple
Time used: 0.043 (sec). Leaf size: 45
dsolve([diff(x__1(t),t)=-4*x__1(t)+2*x__2(t)+1/t,diff(x__2(t),t)=2*x__1(t)-1*x__2(t)+2/t+4],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = \frac {2 \,{\mathrm e}^{-5 t} c_{1}}{5}+\ln \left (-5 t \right )+\frac {c_{2}}{2}+\frac {8 t}{5}-\frac {2}{5} \] \[ x_{2}\relax (t ) = 2 \ln \left (-5 t \right )-\frac {{\mathrm e}^{-5 t} c_{1}}{5}+\frac {16 t}{5}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 83
DSolve[{x1'[t]==-4*x1[t]+2*x2[t]+1/t,x2'[t]==2*x1[t]-1*x2[t]+2/t+4},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{25} \left (40 t+25 \log (t)+10 (2 c_1-c_2) e^{-5 t}-8+5 c_1+10 c_2\right ) \\ \text {x2}(t)\to 2 \log (t)+\frac {1}{5} (c_2-2 c_1) e^{-5 t}+\frac {2}{25} (40 t+2+5 c_1+10 c_2) \\ \end{align*}