Internal problem ID [11026]
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(f).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=\frac {4 y \left (t \right )}{5}+\frac {4 t}{5}\\ y^{\prime }\left (t \right )&=\frac {y \left (t \right )}{5}+\frac {t}{5} \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 31
dsolve([diff(x(t),t)-4*diff(y(t),t)=0,2*diff(x(t),t)-3*diff(y(t),t)=y(t)+t],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -4 t +4 \,{\mathrm e}^{\frac {t}{5}} c_{2} +c_{1} \] \[ y \left (t \right ) = -t -5+{\mathrm e}^{\frac {t}{5}} c_{2} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 43
DSolve[{x'[t]-4*y'[t]==0,2*x'[t]-3*y'[t]==y[t]+t},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -4 t+4 c_2 \left (e^{t/5}-1\right )-20+c_1 \\ y(t)\to -t+c_2 e^{t/5}-5 \\ \end{align*}