Internal problem ID [1590]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 10 Linear system of Differential equations. Section 10.4, constant coefficient
homogeneous system. Page 540
Problem number: section 10.4, problem 2.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\left (t \right )&=-\frac {5 y_{1} \left (t \right )}{4}+\frac {3 y_{2} \left (t \right )}{4}\\ y_{2}^{\prime }\left (t \right )&=\frac {3 y_{1} \left (t \right )}{4}-\frac {5 y_{2} \left (t \right )}{4} \end {align*}
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 35
dsolve([diff(y__1(t),t)=-5/4*y__1(t)+3/4*y__2(t),diff(y__2(t),t)=3/4*y__1(t)-5/4*y__2(t)],[y__1(t), y__2(t)], singsol=all)
\[ y_{1} \left (t \right ) = c_{1} {\mathrm e}^{-\frac {t}{2}}-{\mathrm e}^{-2 t} c_{2} \] \[ y_{2} \left (t \right ) = c_{1} {\mathrm e}^{-\frac {t}{2}}+{\mathrm e}^{-2 t} c_{2} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 76
DSolve[{y1'[t]==-5/4*y1[t]+3/4*y2[t],y2'[t]==3/4*y1[t]-5/4*y2[t]},{y1[t],y2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to \frac {1}{2} e^{-2 t} \left (c_1 \left (e^{3 t/2}+1\right )+c_2 \left (e^{3 t/2}-1\right )\right ) \text {y2}(t)\to \frac {1}{2} e^{-2 t} \left (c_1 \left (e^{3 t/2}-1\right )+c_2 \left (e^{3 t/2}+1\right )\right ) \end{align*}