Internal problem ID [1618]
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 15.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=-3 y_{1}\relax (t )-4 y_{2}\relax (t )\\ y_{2}^{\prime }\relax (t )&=y_{1}\relax (t )-7 y_{2}\relax (t ) \end {align*}
With initial conditions \[ [y_{1}\relax (0) = 2, y_{2}\relax (0) = 3] \]
✓ Solution by Maple
Time used: 0.035 (sec). Leaf size: 28
dsolve([diff(y__1(t),t) = -3*y__1(t)-4*y__2(t), diff(y__2(t),t) = y__1(t)-7*y__2(t), y__1(0) = 2, y__2(0) = 3],[y__1(t), y__2(t)], singsol=all)
\[ y_{1}\relax (t ) = {\mathrm e}^{-5 t} \left (-8 t +2\right ) \] \[ y_{2}\relax (t ) = {\mathrm e}^{-5 t} \left (-4 t +3\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 30
DSolve[{y1'[t]==-3*y1[t]-4*y2[t],y2'[t]==1*y1[t]-7*y2[t]},{y1[0]==2,y2[0]==3},{y1[t],y2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to e^{-5 t} (2-8 t) \\ \text {y2}(t)\to e^{-5 t} (3-4 t) \\ \end{align*}