Internal problem ID [12754]
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 3.1. page 258
Problem number: 29.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=2 x \left (t \right )+3 y\\ y^{\prime }&=x \left (t \right ) \end {align*}
With initial conditions \[ [x \left (0\right ) = 2, y \left (0\right ) = 3] \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
dsolve([diff(x(t),t) = 2*x(t)+3*y(t), diff(y(t),t) = x(t), x(0) = 2, y(0) = 3],[x(t), y(t)], singsol=all)
\begin{align*} x \left (t \right ) = \frac {15 \,{\mathrm e}^{3 t}}{4}-\frac {7 \,{\mathrm e}^{-t}}{4} y \left (t \right ) = \frac {5 \,{\mathrm e}^{3 t}}{4}+\frac {7 \,{\mathrm e}^{-t}}{4} \end{align*}
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 44
DSolve[{x'[t]==2*x[t]+3*y[t],y'[t]==x[t]},{x[0]==2,y[0]==3},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{4} e^{-t} \left (15 e^{4 t}-7\right ) y(t)\to \frac {1}{4} e^{-t} \left (5 e^{4 t}+7\right ) \end{align*}