Internal problem ID [12370]
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(b).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=\frac {t}{3}+\frac {2 x \left (t \right )}{3}+\frac {2 y}{3}\\ y^{\prime }&=\frac {t}{3}-\frac {x \left (t \right )}{3}-\frac {y}{3} \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 45
dsolve([diff(x(t),t)+2*diff(y(t),t)=t,diff(x(t),t)-diff(y(t),t)=x(t)+y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= 3 c_{1} {\mathrm e}^{\frac {t}{3}}-\frac {t^{2}}{2}-4 t +c_{2} \\ y \left (t \right ) &= -\frac {3 c_{1} {\mathrm e}^{\frac {t}{3}}}{2}+2 t -6+\frac {t^{2}}{2}-c_{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.178 (sec). Leaf size: 87
DSolve[{x'[t]+2*y'[t]==t,x'[t]-y'[t]==x[t]+y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -\frac {t^2}{2}-4 t+c_1 \left (2 e^{t/3}-1\right )+2 c_2 \left (e^{t/3}-1\right )-12 \\ y(t)\to \frac {t^2}{2}+2 t-c_1 e^{t/3}-c_2 e^{t/3}+6+c_1+2 c_2 \\ \end{align*}