Internal problem ID [761]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 7.6, Complex Eigenvalues. page 417
Problem number: 11.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=\frac {3 x_{1} \left (t \right )}{4}-2 x_{2} \left (t \right )\\ x_{2}^{\prime }\left (t \right )&=x_{1} \left (t \right )-\frac {5 x_{2} \left (t \right )}{4} \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 45
dsolve([diff(x__1(t),t)=3/4*x__1(t)-2*x__2(t),diff(x__2(t),t)=1*x__1(t)-5/4*x__2(t)],[x__1(t), x__2(t)], singsol=all)
\[ x_{1} \left (t \right ) = {\mathrm e}^{-\frac {t}{4}} \left (\cos \left (t \right ) c_{1} +c_{2} \cos \left (t \right )+c_{1} \sin \left (t \right )-c_{2} \sin \left (t \right )\right ) \] \[ x_{2} \left (t \right ) = {\mathrm e}^{-\frac {t}{4}} \left (c_{1} \sin \left (t \right )+c_{2} \cos \left (t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 56
DSolve[{x1'[t]==3/4*x1[t]-2*x2[t],x2'[t]==1*x1[t]-5/4*x2[t]},{x1[t],x2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {x1}(t)\to e^{-t/4} (c_1 \cos (t)+(c_1-2 c_2) \sin (t)) \text {x2}(t)\to e^{-t/4} (c_2 \cos (t)+(c_1-c_2) \sin (t)) \end{align*}