Internal problem ID [12802]
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: 19.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=4 x \left (t \right )+2 y\\ y^{\prime }&=2 x \left (t \right )+y \end {align*}
With initial conditions \[ [x \left (0\right ) = 1, y \left (0\right ) = 0] \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 24
dsolve([diff(x(t),t) = 4*x(t)+2*y(t), diff(y(t),t) = 2*x(t)+y(t), x(0) = 1, y(0) = 0],[x(t), y(t)], singsol=all)
\begin{align*} x \left (t \right ) = \frac {4 \,{\mathrm e}^{5 t}}{5}+\frac {1}{5} y \left (t \right ) = -\frac {2}{5}+\frac {2 \,{\mathrm e}^{5 t}}{5} \end{align*}
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 32
DSolve[{x'[t]==4*x[t]+2*y[t],y'[t]==2*x[t]+1*y[t]},{x[0]==1,y[0]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{5} \left (4 e^{5 t}+1\right ) y(t)\to \frac {2}{5} \left (e^{5 t}-1\right ) \end{align*}