Internal problem ID [12374]
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}{5}+\frac {4 t}{5}\\ y^{\prime }&=\frac {y}{5}+\frac {t}{5} \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 32
dsolve([diff(x(t),t)-4*diff(y(t),t)=0,2*diff(x(t),t)-3*diff(y(t),t)=y(t)+t],singsol=all)
\begin{align*} x \left (t \right ) &= 5 \,{\mathrm e}^{\frac {t}{5}} c_{1} -4 t +c_{2} \\ y \left (t \right ) &= \frac {5 \,{\mathrm e}^{\frac {t}{5}} c_{1}}{4}-5-t \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 45
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 e^{t/5}-20+c_1-4 c_2 \\ y(t)\to -t+c_2 e^{t/5}-5 \\ \end{align*}