Internal problem ID [324]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 7.3, The eigenvalue method for linear systems. Page 395
Problem number: problem 10.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=-3 x_{1}\relax (t )-2 x_{2}\relax (t )\\ x_{2}^{\prime }\relax (t )&=9 x_{1}\relax (t )+3 x_{2}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 50
dsolve([diff(x__1(t),t)=-3*x__1(t)-2*x__2(t),diff(x__2(t),t)=9*x__1(t)+3*x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = \frac {c_{1} \cos \left (3 t \right )}{3}-\frac {c_{2} \sin \left (3 t \right )}{3}-\frac {c_{1} \sin \left (3 t \right )}{3}-\frac {c_{2} \cos \left (3 t \right )}{3} \] \[ x_{2}\relax (t ) = c_{1} \sin \left (3 t \right )+c_{2} \cos \left (3 t \right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 53
DSolve[{x1'[t]==-3*x1[t]-2*x2[t],x2'[t]==9*x1[t]+3*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to c_1 \cos (3 t)-\frac {1}{3} (3 c_1+2 c_2) \sin (3 t) \\ \text {x2}(t)\to c_2 \cos (3 t)+(3 c_1+c_2) \sin (3 t) \\ \end{align*}