Internal problem ID [11027]
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(g).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=\frac {\sin \left (t \right )}{4}+\frac {x \left (t \right )}{4}+\frac {y \left (t \right )}{4}+\frac {t}{4}\\ y^{\prime }\left (t \right )&=\frac {\sin \left (t \right )}{8}-\frac {3 x \left (t \right )}{8}-\frac {3 y \left (t \right )}{8}-\frac {3 t}{8} \end {align*}
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 51
dsolve([3*diff(x(t),t)+2*diff(y(t),t)=sin(t),diff(x(t),t)-2*diff(y(t),t)=x(t)+y(t)+t],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = \frac {16 \,{\mathrm e}^{-\frac {t}{8}} c_{1}}{3}-\frac {17 \cos \left (t \right )}{65}-\frac {6 \sin \left (t \right )}{65}+8+2 t -c_{2} \] \[ y \left (t \right ) = -8 \,{\mathrm e}^{-\frac {t}{8}} c_{1} +\frac {9 \sin \left (t \right )}{65}-\frac {7 \cos \left (t \right )}{65}-3 t +c_{2} \]
✓ Solution by Mathematica
Time used: 0.232 (sec). Leaf size: 82
DSolve[{x'[t]+2*y'[t]==Sin[t],x'[t]-2*y'[t]==x[t]+y[t]+t},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -2 t-\frac {6 \sin (t)}{17}-\frac {7 \cos (t)}{17}+2 (c_1+c_2) e^{t/4}-8-c_1-2 c_2 \\ y(t)\to t+\frac {3 \sin (t)}{17}-\frac {5 \cos (t)}{17}-(c_1+c_2) e^{t/4}+4+c_1+2 c_2 \\ \end{align*}