Internal problem ID [2271]
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: 6.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} 0&=-5 y^{\prime }\left (t \right )+3 x^{\prime }\left (t \right )+5 y \left (t \right )+5 t\\ 0&=-3 x^{\prime }\left (t \right )+5 y^{\prime }\left (t \right )+2 x \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 28
dsolve([5*diff(y(t),t)-3*diff(x(t),t)-5*y(t)=5*t,3*diff(x(t),t)-5*diff(y(t),t)-2*x(t)=0],singsol=all)
\begin{align*} x \left (t \right ) &= \frac {5}{2}+{\mathrm e}^{\frac {2 t}{5}} c_{1} \\ y \left (t \right ) &= -1-\frac {2 \,{\mathrm e}^{\frac {2 t}{5}} c_{1}}{5}-t \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.137 (sec). Leaf size: 43
DSolve[{5*y'[t]-3*x'[t]-5*y[t]==5*t,3*x'[t]-5*y'[t]-2*x[t]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {5}{6} \left (3+2 c_1 e^{2 t/5}\right ) \\ y(t)\to -t-\frac {2}{3} c_1 e^{2 t/5}-1 \\ \end{align*}