Internal problem ID [11023]
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(c).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=\frac {6}{5}+\frac {3 y \left (t \right )}{5}-\frac {3 t}{5}+x \left (t \right )\\ y^{\prime }\left (t \right )&=\frac {6}{5}-\frac {2 y \left (t \right )}{5}+\frac {2 t}{5} \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 30
dsolve([diff(x(t),t)-diff(y(t),t)=x(t)+y(t)-t,2*diff(x(t),t)+3*diff(y(t),t)=2*x(t)+6],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -\frac {3}{2}-\frac {3 \,{\mathrm e}^{-\frac {2 t}{5}} c_{2}}{7}+c_{1} {\mathrm e}^{t} \] \[ y \left (t \right ) = t +\frac {1}{2}+{\mathrm e}^{-\frac {2 t}{5}} c_{2} \]
✓ Solution by Mathematica
Time used: 0.324 (sec). Leaf size: 53
DSolve[{x'[t]-y'[t]==x[t]+y[t]-t,2*x'[t]+3*y'[t]==2*x[t]+6},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \left (c_1+\frac {3 c_2}{7}\right ) e^t-\frac {3}{7} c_2 e^{-2 t/5}-\frac {3}{2} \\ y(t)\to t+c_2 e^{-2 t/5}+\frac {1}{2} \\ \end{align*}