Internal problem ID [1620]
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 17.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=-7 y_{1} \relax (t )+3 y_{2} \relax (t )\\ y_{2}^{\prime }\relax (t )&=-3 y_{1} \relax (t )-y_{2} \relax (t ) \end {align*}
With initial conditions \[ [y_{1} \relax (0) = 0, y_{2} \relax (0) = 2] \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 25
dsolve([diff(y__1(t),t) = -7*y__1(t)+3*y__2(t), diff(y__2(t),t) = -3*y__1(t)-y__2(t), y__1(0) = 0, y__2(0) = 2],[y__1(t), y__2(t)], singsol=all)
\[ y_{1} \relax (t ) = 6 \,{\mathrm e}^{-4 t} t \] \[ y_{2} \relax (t ) = {\mathrm e}^{-4 t} \left (6 t +2\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 27
DSolve[{y1'[t]==-7*y1[t]+3*y2[t],y2'[t]==-3*y1[t]-1*y2[t]},{y1[0]==0,y2[0]==2},{y1[t],y2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to 6 e^{-4 t} t \\ \text {y2}(t)\to e^{-4 t} (6 t+2) \\ \end{align*}