Internal problem ID [789]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 7.9, Nonhomogeneous Linear Systems. page 447
Problem number: 12.
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 )+\csc \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )-2 x_{2} \left (t \right )+\sec \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.235 (sec). Leaf size: 113
dsolve([diff(x__1(t),t)=2*x__1(t)-5*x__2(t)+csc(t),diff(x__2(t),t)=1*x__1(t)-2*x__2(t)+sec(t)],singsol=all)
\begin{align*} x_{1} \left (t \right ) &= \ln \left (\sin \left (t \right )\right ) \cos \left (t \right )-5 \cos \left (t \right ) \ln \left (\cos \left (t \right )\right )+c_{1} \cos \left (t \right )-2 \cos \left (t \right ) t +2 \ln \left (\sin \left (t \right )\right ) \sin \left (t \right )+c_{2} \sin \left (t \right )-4 \sin \left (t \right ) t +\cos \left (t \right ) \\ x_{2} \left (t \right ) &= -2 \cos \left (t \right ) \ln \left (\cos \left (t \right )\right )+\frac {2 c_{1} \cos \left (t \right )}{5}-\frac {c_{2} \cos \left (t \right )}{5}+\ln \left (\sin \left (t \right )\right ) \sin \left (t \right )-\sin \left (t \right ) \ln \left (\cos \left (t \right )\right )+\frac {c_{1} \sin \left (t \right )}{5}+\frac {2 c_{2} \sin \left (t \right )}{5}-2 \sin \left (t \right ) t -\frac {\cos \left (t \right )^{2}}{5 \sin \left (t \right )}+\frac {2 \cos \left (t \right )}{5}+\frac {\csc \left (t \right )}{5} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 79
DSolve[{x1'[t]==2*x1[t]-5*x2[t]+Csc[t],x2'[t]==1*x1[t]-2*x2[t]+Sec[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \sin (t) (-4 t+2 \log (\sin (t))+2 c_1-5 c_2)+\cos (t) (-2 t+\log (\sin (t))-5 \log (\cos (t))+c_1) \\ \text {x2}(t)\to \cos (t) (-2 \log (\cos (t))+c_2)+\sin (t) (-2 t+\log (\sin (t))-\log (\cos (t))+c_1-2 c_2) \\ \end{align*}