21.2 problem section 10.4, problem 2

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 }\relax (t )&=-\frac {5 y_{1} \relax (t )}{4}+\frac {3 y_{2} \relax (t )}{4}\\ y_{2}^{\prime }\relax (t )&=\frac {3 y_{1} \relax (t )}{4}-\frac {5 y_{2} \relax (t )}{4} \end {align*}

Solution by Maple

Time used: 0.063 (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)
 

\[ y_{1} \relax (t ) = -c_{1} {\mathrm e}^{-2 t}+c_{2} {\mathrm e}^{-\frac {t}{2}} \] \[ y_{2} \relax (t ) = c_{1} {\mathrm e}^{-2 t}+c_{2} {\mathrm e}^{-\frac {t}{2}} \]

Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 66

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+c_2) e^{3 t/2}+c_1-c_2\right ) \\ \text {y2}(t)\to \frac {1}{2} e^{-2 t} \left ((c_1+c_2) e^{3 t/2}-c_1+c_2\right ) \\ \end{align*}