Internal problem ID [10540]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY.
2015.
Section: Chapter 4, Linear Systems. Exercises page 237
Problem number: 4(d).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-5 x \left (t \right )+3 y \left (t \right )\\ y^{\prime }\left (t \right )&=2 x \left (t \right )-10 y \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 36
dsolve([diff(x(t),t)=-5*x(t)+3*y(t),diff(y(t),t)=2*x(t)-10*y(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -\frac {c_{1} {\mathrm e}^{-11 t}}{2}+3 c_{2} {\mathrm e}^{-4 t} \] \[ y \left (t \right ) = c_{1} {\mathrm e}^{-11 t}+c_{2} {\mathrm e}^{-4 t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 69
DSolve[{x'[t]==-5*x[t]+3*y[t],y'[t]==2*x[t]-10*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{7} e^{-11 t} \left (3 (2 c_1+c_2) e^{7 t}+c_1-3 c_2\right ) \\ y(t)\to \frac {1}{7} e^{-11 t} \left (2 c_1 \left (e^{7 t}-1\right )+c_2 \left (e^{7 t}+6\right )\right ) \\ \end{align*}