Internal problem ID [788]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 7.9, Nonhomogeneous Linear Systems. page 447
Problem number: 11.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=2 x_{1}\relax (t )-5 x_{2}\relax (t )\\ x_{2}^{\prime }\relax (t )&=x_{1}\relax (t )-2 x_{2}\relax (t )+\cos \relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.079 (sec). Leaf size: 60
dsolve([diff(x__1(t),t)=2*x__1(t)-5*x__2(t)+0,diff(x__2(t),t)=1*x__1(t)-2*x__2(t)+cos(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = 2 \cos \relax (t ) c_{1}+c_{2} \cos \relax (t )-c_{1} \sin \relax (t )+2 \sin \relax (t ) c_{2}-\frac {5 \sin \relax (t ) t}{2}-\frac {5 \cos \relax (t )}{2} \] \[ x_{2}\relax (t ) = \sin \relax (t ) c_{2}+\cos \relax (t ) c_{1}+\frac {\cos \relax (t ) t}{2}-\cos \relax (t )-\sin \relax (t ) t \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 60
DSolve[{x1'[t]==2*x1[t]-5*x2[t]+0,x2'[t]==1*x1[t]-2*x2[t]-Cos[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \left (\frac {5}{2}+c_1\right ) \cos (t)+\frac {1}{2} (5 t+4 c_1-10 c_2) \sin (t) \\ \text {x2}(t)\to \left (-\frac {t}{2}+1+c_2\right ) \cos (t)+(t+c_1-2 c_2) \sin (t) \\ \end{align*}