Internal problem ID [2270]
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: 5.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-\frac {3 x \left (t \right )}{2}+\frac {y \left (t \right )}{2}+\frac {{\mathrm e}^{t}}{2}\\ y^{\prime }\left (t \right )&=\frac {5 x \left (t \right )}{3}-\frac {y \left (t \right )}{3}-\frac {2 t}{3} \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 50
dsolve([2*diff(x(t),t)+3*x(t)-y(t)=exp(t),5*x(t)-3*diff(y(t),t)=y(t)+2*t],[x(t), y(t)], singsol=all)
\begin{align*} x \left (t \right ) = \frac {3 \,{\mathrm e}^{\frac {t}{6}} c_{2}}{10}-{\mathrm e}^{-2 t} c_{1} +\frac {11}{2}+\frac {4 \,{\mathrm e}^{t}}{15}+t y \left (t \right ) = {\mathrm e}^{\frac {t}{6}} c_{2} +{\mathrm e}^{-2 t} c_{1} +3 t +\frac {37}{2}+\frac {{\mathrm e}^{t}}{3} \end{align*}
✓ Solution by Mathematica
Time used: 0.685 (sec). Leaf size: 105
DSolve[{2*x'[t]+3*x[t]-y[t]==Exp[t],5*x[t]-3*y'[t]==y[t]+2*t},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to t+\frac {4 e^t}{15}+\frac {1}{13} (10 c_1-3 c_2) e^{-2 t}+\frac {3}{13} (c_1+c_2) e^{t/6}+\frac {11}{2} y(t)\to \frac {1}{78} e^{-2 t} \left (39 e^{2 t} (6 t+37)+26 e^{3 t}+60 (c_1+c_2) e^{13 t/6}-60 c_1+18 c_2\right ) \end{align*}