Internal problem ID [12375]
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}{4}+\frac {t}{4}\\ y^{\prime }&=\frac {\sin \left (t \right )}{8}-\frac {3 x \left (t \right )}{8}-\frac {3 y}{8}-\frac {3 t}{8} \end {align*}
✓ Solution by Maple
Time used: 0.109 (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],singsol=all)
\begin{align*} x \left (t \right ) &= -8 \,{\mathrm e}^{-\frac {t}{8}} c_{1} -\frac {6 \sin \left (t \right )}{65}-\frac {17 \cos \left (t \right )}{65}+2 t +c_{2} \\ y \left (t \right ) &= 12 \,{\mathrm e}^{-\frac {t}{8}} c_{1} -\frac {7 \cos \left (t \right )}{65}+\frac {9 \sin \left (t \right )}{65}+8-3 t -c_{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.358 (sec). Leaf size: 98
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 e^{t/4}+2 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 e^{t/4}-c_2 e^{t/4}+4+c_1+2 c_2 \\ \end{align*}