Internal problem ID [1617]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 10 Linear system of Differential equations. Section 10.5, constant coefficient
homogeneous system II. Page 555
Problem number: section 10.5, problem 14.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=15 y_{1}\relax (t )-9 y_{2}\relax (t )\\ y_{2}^{\prime }\relax (t )&=16 y_{1}\relax (t )-9 y_{2}\relax (t ) \end {align*}
With initial conditions \[ [y_{1}\relax (0) = 5, y_{2}\relax (0) = 8] \]
✓ Solution by Maple
Time used: 0.037 (sec). Leaf size: 29
dsolve([diff(y__1(t),t) = 15*y__1(t)-9*y__2(t), diff(y__2(t),t) = 16*y__1(t)-9*y__2(t), y__1(0) = 5, y__2(0) = 8],[y__1(t), y__2(t)], singsol=all)
\[ y_{1}\relax (t ) = \frac {{\mathrm e}^{3 t} \left (-192 t +80\right )}{16} \] \[ y_{2}\relax (t ) = {\mathrm e}^{3 t} \left (-16 t +8\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 31
DSolve[{y1'[t]==15*y1[t]-9*y2[t],y2'[t]==16*y1[t]-9*y2[t]},{y1[0]==5,y2[0]==8},{y1[t],y2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to e^{3 t} (5-12 t) \\ \text {y2}(t)\to -8 e^{3 t} (2 t-1) \\ \end{align*}