Internal problem ID [2269]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 26, page 115
Problem number: 4.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-y \left (t \right )+x \left (t \right )+2 \sin \left (t \right )\\ y^{\prime }\left (t \right )&=4 y \left (t \right )-4 x \left (t \right )-2 \sin \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 42
dsolve([diff(x(t),t)-x(t)+y(t)=2*sin(t),diff(x(t),t)+diff(y(t),t)=3*y(t)-3*x(t)],[x(t), y(t)], singsol=all)
\begin{align*} x \left (t \right ) = -\frac {{\mathrm e}^{5 t} c_{1}}{20}-\frac {16 \cos \left (t \right )}{13}-\frac {2 \sin \left (t \right )}{13}+c_{2} y \left (t \right ) = \frac {{\mathrm e}^{5 t} c_{1}}{5}+\frac {8 \sin \left (t \right )}{13}-\frac {14 \cos \left (t \right )}{13}+c_{2} \end{align*}
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 80
DSolve[{x'[t]-x[t]+y[t]==2*Sin[t],x'[t]+y'[t]==3*y[t]-3*x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{65} \left (-10 \sin (t)-80 \cos (t)+13 c_1 \left (e^{5 t}+4\right )-13 c_2 \left (e^{5 t}-1\right )\right ) y(t)\to \frac {1}{65} \left (40 \sin (t)-70 \cos (t)-52 c_1 \left (e^{5 t}-1\right )+13 c_2 \left (4 e^{5 t}+1\right )\right ) \end{align*}