Internal problem ID [13081]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 3. Linear Systems. Exercises section 3.2. page 277
Problem number: 6.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=5 x \left (t \right )+4 y\\ y^{\prime }&=9 x \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 35
dsolve([diff(x(t),t)=5*x(t)+4*y(t),diff(y(t),t)=9*x(t)],singsol=all)
\begin{align*} x \left (t \right ) &= -\frac {4 \,{\mathrm e}^{-4 t} c_{1}}{9}+c_{2} {\mathrm e}^{9 t} \\ y \left (t \right ) &= {\mathrm e}^{-4 t} c_{1} +c_{2} {\mathrm e}^{9 t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 74
DSolve[{x'[t]==5*x[t]+4*y[t],y'[t]==9*x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{13} e^{-4 t} \left (c_1 \left (9 e^{13 t}+4\right )+4 c_2 \left (e^{13 t}-1\right )\right ) \\ y(t)\to \frac {1}{13} e^{-4 t} \left (9 c_1 \left (e^{13 t}-1\right )+c_2 \left (4 e^{13 t}+9\right )\right ) \\ \end{align*}