Internal problem ID [1591]
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 3.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=-\frac {4 y_{1} \relax (t )}{5}+\frac {3 y_{2} \relax (t )}{5}\\ y_{2}^{\prime }\relax (t )&=-\frac {2 y_{1} \relax (t )}{5}-\frac {11 y_{2} \relax (t )}{5} \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 36
dsolve([diff(y__1(t),t)=-4/5*y__1(t)+3/5*y__2(t),diff(y__2(t),t)=-2/5*y__1(t)-11/5*y__2(t)],[y__1(t), y__2(t)], singsol=all)
\[ y_{1} \relax (t ) = -\frac {c_{1} {\mathrm e}^{-2 t}}{2}-3 c_{2} {\mathrm e}^{-t} \] \[ y_{2} \relax (t ) = c_{1} {\mathrm e}^{-2 t}+c_{2} {\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 67
DSolve[{y1'[t]==-4/5*y1[t]+3/5*y2[t],y2'[t]==-2/5*y1[t]-11/5*y2[t]},{y1[t],y2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to \frac {1}{5} e^{-2 t} \left (c_1 \left (6 e^t-1\right )+3 c_2 \left (e^t-1\right )\right ) \\ \text {y2}(t)\to \frac {1}{5} e^{-2 t} \left (-(2 c_1+c_2) e^t+2 c_1+6 c_2\right ) \\ \end{align*}