Internal problem ID [755]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 7.6, Complex Eigenvalues. page 417
Problem number: 5.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\relax (t )&=x_{1}\relax (t )-x_{2}\relax (t )\\ x_{2}^{\prime }\relax (t )&=5 x_{1}\relax (t )-3 x_{2}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.026 (sec). Leaf size: 48
dsolve([diff(x__1(t),t)=1*x__1(t)-1*x__2(t),diff(x__2(t),t)=5*x__1(t)-3*x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1}\relax (t ) = \frac {{\mathrm e}^{-t} \left (\cos \relax (t ) c_{1}-\sin \relax (t ) c_{2}+2 c_{1} \sin \relax (t )+2 c_{2} \cos \relax (t )\right )}{5} \] \[ x_{2}\relax (t ) = {\mathrm e}^{-t} \left (c_{1} \sin \relax (t )+c_{2} \cos \relax (t )\right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 55
DSolve[{x1'[t]==1*x1[t]-1*x2[t],x2'[t]==5*x1[t]-3*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{-t} (c_1 \cos (t)+(2 c_1-c_2) \sin (t)) \\ \text {x2}(t)\to e^{-t} (5 c_1 \sin (t)+c_2 (\cos (t)-2 \sin (t))) \\ \end{align*}