Internal problem ID [10206]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1883.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )-y^{\prime }\left (t \right )+x \left (t \right )&=2 t\\ x^{\prime \prime }\left (t \right )+y^{\prime }\left (t \right )-9 x \left (t \right )+3 y \left (t \right )&=\sin \left (2 t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.204 (sec). Leaf size: 80
dsolve([diff(x(t),t)-diff(y(t),t)+x(t)=2*t,diff(x(t),t$2)+diff(y(t),t)-9*x(t)+3*y(t)=sin(2*t)],singsol=all)
\begin{align*} x \left (t \right ) &= -\frac {36 \sin \left (2 t \right )}{325}-\frac {2 \cos \left (2 t \right )}{325}+\frac {c_{1} {\mathrm e}^{t}}{2}+\frac {3 c_{2} {\mathrm e}^{-3 t}}{2}+\frac {c_{3} {\mathrm e}^{t}}{4}+\frac {c_{3} t \,{\mathrm e}^{t}}{2}+2 t +4 \\ y \left (t \right ) &= 6 t +10-\frac {37 \sin \left (2 t \right )}{325}+\frac {16 \cos \left (2 t \right )}{325}+c_{1} {\mathrm e}^{t}+c_{2} {\mathrm e}^{-3 t}+c_{3} t \,{\mathrm e}^{t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.889 (sec). Leaf size: 170
DSolve[{x'[t]-y'[t]+x[t]==2*t,x''[t]+y'[t]-9*x[t]+3*y[t]==Sin[2*t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -\frac {36}{325} \sin (2 t)-\frac {2}{325} \cos (2 t)+\frac {1}{16} e^{-3 t} \left (32 e^{3 t} (t+2)+e^{4 t} (c_1 (20 t+7)+c_2 (4 t+3)+3 c_3 (1-4 t))+9 c_1-3 (c_2+c_3)\right ) \\ y(t)\to -\frac {37}{325} \sin (2 t)+\frac {16}{325} \cos (2 t)+\frac {1}{8} e^{-3 t} \left (16 e^{3 t} (3 t+5)+e^{4 t} (c_1 (20 t-3)+4 c_2 t-12 c_3 t+c_2+9 c_3)+3 c_1-c_2-c_3\right ) \\ \end{align*}