Internal problem ID [13106]
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 3.4 page 310
Problem number: 11.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-3 x \left (t \right )-5 y\\ y^{\prime }&=3 x \left (t \right )+y \end {align*}
With initial conditions \[ [x \left (0\right ) = 4, y \left (0\right ) = 0] \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 48
dsolve([diff(x(t),t) = -3*x(t)-5*y(t), diff(y(t),t) = 3*x(t)+y(t), x(0) = 4, y(0) = 0], singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{-t} \left (-\frac {8 \sqrt {11}\, \sin \left (\sqrt {11}\, t \right )}{11}+4 \cos \left (\sqrt {11}\, t \right )\right ) \\ y \left (t \right ) &= \frac {12 \,{\mathrm e}^{-t} \sqrt {11}\, \sin \left (\sqrt {11}\, t \right )}{11} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 63
DSolve[{x'[t]==-3*x[t]-5*y[t],y'[t]==3*x[t]+1*y[t]},{x[0]==4,y[0]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {4}{11} e^{-t} \left (11 \cos \left (\sqrt {11} t\right )-2 \sqrt {11} \sin \left (\sqrt {11} t\right )\right ) \\ y(t)\to \frac {12 e^{-t} \sin \left (\sqrt {11} t\right )}{\sqrt {11}} \\ \end{align*}