Internal problem ID [13108]
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: 13.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=2 x \left (t \right )-6 y\\ y^{\prime }&=2 x \left (t \right )+y \end {align*}
With initial conditions \[ [x \left (0\right ) = 2, y \left (0\right ) = 1] \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 63
dsolve([diff(x(t),t) = 2*x(t)-6*y(t), diff(y(t),t) = 2*x(t)+y(t), x(0) = 2, y(0) = 1], singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{\frac {3 t}{2}} \left (-\frac {10 \sqrt {47}\, \sin \left (\frac {\sqrt {47}\, t}{2}\right )}{47}+2 \cos \left (\frac {\sqrt {47}\, t}{2}\right )\right ) \\ y \left (t \right ) &= \frac {{\mathrm e}^{\frac {3 t}{2}} \left (\frac {84 \sqrt {47}\, \sin \left (\frac {\sqrt {47}\, t}{2}\right )}{47}+12 \cos \left (\frac {\sqrt {47}\, t}{2}\right )\right )}{12} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 94
DSolve[{x'[t]==2*x[t]-6*y[t],y'[t]==2*x[t]+1*y[t]},{x[0]==2,y[0]==1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {2}{47} e^{3 t/2} \left (47 \cos \left (\frac {\sqrt {47} t}{2}\right )-5 \sqrt {47} \sin \left (\frac {\sqrt {47} t}{2}\right )\right ) \\ y(t)\to \frac {1}{47} e^{3 t/2} \left (7 \sqrt {47} \sin \left (\frac {\sqrt {47} t}{2}\right )+47 \cos \left (\frac {\sqrt {47} t}{2}\right )\right ) \\ \end{align*}