Internal problem ID [1608]
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 5.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=4 y_{1}\relax (t )+12 y_{2}\relax (t )\\ y_{2}^{\prime }\relax (t )&=-3 y_{1}\relax (t )-8 y_{2}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 33
dsolve([diff(y__1(t),t)=4*y__1(t)+12*y__2(t),diff(y__2(t),t)=-3*y__1(t)-8*y__2(t)],[y__1(t), y__2(t)], singsol=all)
\[ y_{1}\relax (t ) = -\frac {{\mathrm e}^{-2 t} \left (6 c_{2} t +6 c_{1}+c_{2}\right )}{3} \] \[ y_{2}\relax (t ) = {\mathrm e}^{-2 t} \left (c_{2} t +c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 46
DSolve[{y1'[t]==4*y1[t]+12*y2[t],y2'[t]==-3*y1[t]-8*y2[t]},{y1[t],y2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to e^{-2 t} (6 c_1 t+12 c_2 t+c_1) \\ \text {y2}(t)\to e^{-2 t} (c_2-3 (c_1+2 c_2) t) \\ \end{align*}