Internal problem ID [1607]
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 4.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=3 y_{1}\relax (t )+y_{2}\relax (t )\\ y_{2}^{\prime }\relax (t )&=-y_{1}\relax (t )+y_{2}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.029 (sec). Leaf size: 30
dsolve([diff(y__1(t),t)=3*y__1(t)+1*y__2(t),diff(y__2(t),t)=-1*y__1(t)+1*y__2(t)],[y__1(t), y__2(t)], singsol=all)
\[ y_{1}\relax (t ) = -{\mathrm e}^{2 t} \left (c_{2} t +c_{1}+c_{2}\right ) \] \[ y_{2}\relax (t ) = {\mathrm e}^{2 t} \left (c_{2} t +c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 42
DSolve[{y1'[t]==3*y1[t]+1*y2[t],y2'[t]==-1*y1[t]+1*y2[t]},{y1[t],y2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to e^{2 t} (c_1 (t+1)+c_2 t) \\ \text {y2}(t)\to e^{2 t} (c_2-(c_1+c_2) t) \\ \end{align*}