Internal problem ID [11022]
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 \left (t \right )}{3}\\ y^{\prime }\left (t \right )&=\frac {t}{3}-\frac {x \left (t \right )}{3}-\frac {y \left (t \right )}{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)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -4 t -6 \,{\mathrm e}^{\frac {t}{3}} c_{1} -6-\frac {t^{2}}{2}-c_{2} \] \[ y \left (t \right ) = \frac {t^{2}}{2}+3 \,{\mathrm e}^{\frac {t}{3}} c_{1} +2 t +c_{2} \]
✓ Solution by Mathematica
Time used: 0.117 (sec). Leaf size: 71
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 {1}{2} t (t+8)+2 (c_1+c_2) e^{t/3}-c_1-2 (6+c_2) \\ y(t)\to \frac {1}{2} t (t+4)-(c_1+c_2) e^{t/3}+6+c_1+2 c_2 \\ \end{align*}