Internal problem ID [11548]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 4, Linear Systems. Exercises page 218
Problem number: 2(b).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }&=x\\ y^{\prime }\left (t \right )&=3 x-4 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
dsolve([diff(x(t),t)=x(t),diff(y(t),t)=3*x(t)-4*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{t} \\ y \left (t \right ) &= \frac {3 c_{2} {\mathrm e}^{t}}{5}+{\mathrm e}^{-4 t} c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 149
DSolve[{x'[t]==x[t]+y[t],y'[t]==3*x[t]-4*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{74} e^{-\frac {1}{2} \left (3+\sqrt {37}\right ) t} \left (c_1 \left (\left (37+5 \sqrt {37}\right ) e^{\sqrt {37} t}+37-5 \sqrt {37}\right )+2 \sqrt {37} c_2 \left (e^{\sqrt {37} t}-1\right )\right ) \\ y(t)\to \frac {1}{74} e^{-\frac {1}{2} \left (3+\sqrt {37}\right ) t} \left (6 \sqrt {37} c_1 \left (e^{\sqrt {37} t}-1\right )-c_2 \left (\left (5 \sqrt {37}-37\right ) e^{\sqrt {37} t}-37-5 \sqrt {37}\right )\right ) \\ \end{align*}