Internal problem ID [12372]
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(d).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=\frac {2 t}{7}+\frac {y}{7}\\ y^{\prime }&=-\frac {3 t}{7}+\frac {2 y}{7} \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 37
dsolve([2*diff(x(t),t)-diff(y(t),t)=t,3*diff(x(t),t)+2*diff(y(t),t)=y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= \frac {t^{2}}{4}+\frac {7 \,{\mathrm e}^{\frac {2 t}{7}} c_{1}}{2}+\frac {3 t}{4}+c_{2} \\ y \left (t \right ) &= \frac {3 t}{2}+7 \,{\mathrm e}^{\frac {2 t}{7}} c_{1} +\frac {21}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.129 (sec). Leaf size: 60
DSolve[{2*x'[t]-y'[t]==t,3*x'[t]+2*y'[t]==y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{8} \left (2 t^2+6 t+4 c_2 e^{2 t/7}+21+8 c_1-4 c_2\right ) \\ y(t)\to \frac {3 t}{2}+c_2 e^{2 t/7}+\frac {21}{4} \\ \end{align*}