Internal problem ID [12801]
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 3.5 page 327
Problem number: 18.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=2 x \left (t \right )+4 y\\ y^{\prime }&=3 x \left (t \right )+6 y \end {align*}
With initial conditions \[ [x \left (0\right ) = 1, y \left (0\right ) = 0] \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
dsolve([diff(x(t),t) = 2*x(t)+4*y(t), diff(y(t),t) = 3*x(t)+6*y(t), x(0) = 1, y(0) = 0],[x(t), y(t)], singsol=all)
\begin{align*} x \left (t \right ) = \frac {{\mathrm e}^{8 t}}{4}+\frac {3}{4} y \left (t \right ) = -\frac {3}{8}+\frac {3 \,{\mathrm e}^{8 t}}{8} \end{align*}
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 30
DSolve[{x'[t]==2*x[t]+4*y[t],y'[t]==3*x[t]+6*y[t]},{x[0]==1,y[0]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{4} \left (e^{8 t}+3\right ) y(t)\to \frac {3}{8} \left (e^{8 t}-1\right ) \end{align*}