Internal problem ID [328]
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 14.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=3 x_{1}\relax (t )-4 x_{2}\relax (t )\\ x_{2}^{\prime }\relax (t )&=4 x_{1}\relax (t )+3 x_{2}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 45
dsolve([diff(x__1(t),t)=3*x__1(t)-4*x__2(t),diff(x__2(t),t)=4*x__1(t)+3*x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = {\mathrm e}^{3 t} \left (c_{1} \cos \left (4 t \right )-c_{2} \sin \left (4 t \right )\right ) \] \[ x_{2}\relax (t ) = {\mathrm e}^{3 t} \left (c_{1} \sin \left (4 t \right )+c_{2} \cos \left (4 t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 51
DSolve[{x1'[t]==3*x1[t]-4*x2[t],x2'[t]==4*x1[t]+3*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{3 t} (c_1 \cos (4 t)-c_2 \sin (4 t)) \\ \text {x2}(t)\to e^{3 t} (c_2 \cos (4 t)+c_1 \sin (4 t)) \\ \end{align*}