Internal problem ID [13111]
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: 26.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-3 x \left (t \right )+10 y\\ y^{\prime }&=-x \left (t \right )+3 y \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 38
dsolve([diff(x(t),t)=-3*x(t)+10*y(t),diff(y(t),t)=-x(t)+3*y(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{1} \sin \left (t \right )+c_{2} \cos \left (t \right ) \\ y \left (t \right ) &= \frac {c_{1} \cos \left (t \right )}{10}-\frac {c_{2} \sin \left (t \right )}{10}+\frac {3 c_{1} \sin \left (t \right )}{10}+\frac {3 c_{2} \cos \left (t \right )}{10} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 42
DSolve[{x'[t]==-3*x[t]+10*y[t],y'[t]==-x[t]+3*y[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 10 c_2 \sin (t)+c_1 (\cos (t)-3 \sin (t)) \\ y(t)\to c_2 (3 \sin (t)+\cos (t))-c_1 \sin (t) \\ \end{align*}