Internal problem ID [1619]
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 16.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=-7 y_{1}\relax (t )+24 y_{2}\relax (t )\\ y_{2}^{\prime }\relax (t )&=-6 y_{1}\relax (t )+17 y_{2}\relax (t ) \end {align*}
With initial conditions \[ [y_{1}\relax (0) = 3, y_{2}\relax (0) = 1] \]
✓ Solution by Maple
Time used: 0.033 (sec). Leaf size: 29
dsolve([diff(y__1(t),t) = -7*y__1(t)+24*y__2(t), diff(y__2(t),t) = -6*y__1(t)+17*y__2(t), y__1(0) = 3, y__2(0) = 1],[y__1(t), y__2(t)], singsol=all)
\[ y_{1}\relax (t ) = \frac {{\mathrm e}^{5 t} \left (-72 t +18\right )}{6} \] \[ y_{2}\relax (t ) = {\mathrm e}^{5 t} \left (-6 t +1\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 31
DSolve[{y1'[t]==-7*y1[t]+24*y2[t],y2'[t]==-6*y1[t]+17*y2[t]},{y1[0]==3,y2[0]==1},{y1[t],y2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to -3 e^{5 t} (4 t-1) \\ \text {y2}(t)\to e^{5 t} (1-6 t) \\ \end{align*}