Internal problem ID [2268]
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: 3.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-2 x \left (t \right )+3 t\\ y^{\prime }\left (t \right )&=x \left (t \right )-\frac {3 t}{2}-\frac {y \left (t \right )}{2}+\cos \left (t \right )^{2}-\frac {1}{2} \end {align*}
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 46
dsolve([diff(x(t),t)+2*x(t)=3*t,diff(x(t),t)+2*diff(y(t),t)+y(t)=cos(2*t)],[x(t), y(t)], singsol=all)
\begin{align*} x \left (t \right ) = \frac {3 t}{2}-\frac {3 \,{\mathrm e}^{-2 t} c_{1}}{2}-\frac {3}{4} y \left (t \right ) = {\mathrm e}^{-\frac {t}{2}} c_{2} +{\mathrm e}^{-2 t} c_{1} -\frac {3}{2}+\frac {\cos \left (2 t \right )}{17}+\frac {4 \sin \left (2 t \right )}{17} \end{align*}
✓ Solution by Mathematica
Time used: 0.348 (sec). Leaf size: 74
DSolve[{x'[t]+2*x[t]==3*t,x'[t]+2*y'[t]+y[t]==Cos[2*t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {3 t}{2}+c_1 e^{-2 t}-\frac {3}{4} y(t)\to \frac {4}{17} \sin (2 t)+\frac {1}{17} \cos (2 t)+\frac {1}{6} \left (-4 c_1 e^{-2 t}+(4 c_1+6 c_2) e^{-t/2}-9\right ) \end{align*}