Internal problem ID [780]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 7.9, Nonhomogeneous Linear Systems. page 447
Problem number: 3.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=2 x_{1} \left (t \right )-5 x_{2} \left (t \right )-\cos \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )-2 x_{2} \left (t \right )+\sin \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 60
dsolve([diff(x__1(t),t)=2*x__1(t)-5*x__2(t)-cos(t),diff(x__2(t),t)=1*x__1(t)-2*x__2(t)+sin(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= c_{2} \sin \left (t \right )-\sin \left (t \right ) t +c_{1} \cos \left (t \right )+2 \cos \left (t \right ) t -\cos \left (t \right ) \\ x_{2} \left (t \right ) &= \frac {c_{1} \sin \left (t \right )}{5}+\frac {2 c_{2} \sin \left (t \right )}{5}+\frac {2 c_{1} \cos \left (t \right )}{5}-\frac {c_{2} \cos \left (t \right )}{5}+\cos \left (t \right ) t -\cos \left (t \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.069 (sec). Leaf size: 61
DSolve[{x1'[t]==2*x1[t]-5*x2[t]-Cos[t],x2'[t]==1*x1[t]-2*x2[t]+Sin[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \left (2 t-\frac {1}{2}+c_1\right ) \cos (t)-(t-1-2 c_1+5 c_2) \sin (t) \\ \text {x2}(t)\to (t-1+c_2) \cos (t)+\frac {1}{2} (1+2 c_1-4 c_2) \sin (t) \\ \end{align*}