Internal problem ID [11579]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 4, Linear Systems. Exercises page 244
Problem number: 7.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }&=x-3 y \left (t \right )\\ y^{\prime }\left (t \right )&=3 x+7 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 35
dsolve([diff(x(t),t)=x(t)-3*y(t),diff(y(t),t)=3*x(t)+7*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -\frac {{\mathrm e}^{4 t} \left (3 t c_{2} +3 c_{1} -c_{2} \right )}{3} \] \[ y \left (t \right ) = {\mathrm e}^{4 t} \left (t c_{2} +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 46
DSolve[{x'[t]==x[t]-3*y[t],y'[t]==3*x[t]+7*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -e^{4 t} (c_1 (3 t-1)+3 c_2 t) y(t)\to e^{4 t} (3 (c_1+c_2) t+c_2) \end{align*}