Internal problem ID [12373]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A.
Dobrushkin. CRC Press 2015
Section: Chapter 6.4 Reduction to a single ODE. Problems page 415
Problem number: Problem 4(e).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=\frac {3 t}{4}-\frac {x \left (t \right )}{4}-\frac {y}{4}\\ y^{\prime }&=\frac {5 t}{4}-\frac {3 x \left (t \right )}{4}-\frac {3 y}{4} \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 45
dsolve([5*diff(x(t),t)-3*diff(y(t),t)=x(t)+y(t),3*diff(x(t),t)-diff(y(t),t)=t],singsol=all)
\begin{align*} x \left (t \right ) &= \frac {t^{2}}{8}-{\mathrm e}^{-t} c_{1} +\frac {t}{2}+c_{2} \\ y \left (t \right ) &= \frac {3 t}{2}-3 \,{\mathrm e}^{-t} c_{1} -2-\frac {t^{2}}{8}-c_{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.075 (sec). Leaf size: 75
DSolve[{5*x'[t]-3*y'[t]==x[t]+y[t],3*x'[t]-y'[t]==t},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{8} \left (t^2+4 t+2 (c_1+c_2) e^{-t}-4+6 c_1-2 c_2\right ) \\ y(t)\to \frac {1}{8} \left (-t^2+12 t+2 \left (3 (c_1+c_2) e^{-t}-6-3 c_1+c_2\right )\right ) \\ \end{align*}