Internal problem ID [13073]
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: 28.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-2 x \left (t \right )-3 y\\ y^{\prime }&=3 x \left (t \right )-2 y \end {align*}
With initial conditions \[ [x \left (0\right ) = 2, y \left (0\right ) = 3] \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 45
dsolve([diff(x(t),t) = -2*x(t)-3*y(t), diff(y(t),t) = 3*x(t)-2*y(t), x(0) = 2, y(0) = 3], singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{-2 t} \left (-3 \sin \left (3 t \right )+2 \cos \left (3 t \right )\right ) \\ y \left (t \right ) &= -{\mathrm e}^{-2 t} \left (-3 \cos \left (3 t \right )-2 \sin \left (3 t \right )\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 46
DSolve[{x'[t]==-2*x[t]-3*y[t],y'[t]==3*x[t]-2*y[t]},{x[0]==2,y[0]==3},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to e^{-2 t} (2 \cos (3 t)-3 \sin (3 t)) \\ y(t)\to e^{-2 t} (2 \sin (3 t)+3 \cos (3 t)) \\ \end{align*}