Internal problem ID [329]
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 15.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=7 x_{1}\relax (t )-5 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: 0.016 (sec). Leaf size: 59
dsolve([diff(x__1(t),t)=7*x__1(t)-5*x__2(t),diff(x__2(t),t)=4*x__1(t)+3*x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = \frac {{\mathrm e}^{5 t} \left (2 c_{1} \cos \left (4 t \right )-2 c_{2} \sin \left (4 t \right )+c_{1} \sin \left (4 t \right )+c_{2} \cos \left (4 t \right )\right )}{2} \] \[ x_{2}\relax (t ) = {\mathrm e}^{5 t} \left (c_{1} \sin \left (4 t \right )+c_{2} \cos \left (4 t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 72
DSolve[{x1'[t]==7*x1[t]-5*x2[t],x2'[t]==4*x1[t]+3*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to \frac {1}{4} e^{5 t} (4 c_1 \cos (4 t)+(2 c_1-5 c_2) \sin (4 t)) \\ \text {x2}(t)\to \frac {1}{2} e^{5 t} (2 c_2 \cos (4 t)+(2 c_1-c_2) \sin (4 t)) \\ \end{align*}