Internal problem ID [1589]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 10 Linear system of Differential equations. Section 10.4, constant coefficient
homogeneous system. Page 540
Problem number: section 10.4, problem 1.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\relax (t )&=y_{1}\relax (t )+2 y_{2}\relax (t )\\ y_{2}^{\prime }\relax (t )&=2 y_{1}\relax (t )+y_{2}\relax (t ) \end {align*}
✓ Solution by Maple
Time used: 0.037 (sec). Leaf size: 35
dsolve([diff(y__1(t),t)=y__1(t)+2*y__2(t),diff(y__2(t),t)=2*y__1(t)+1*y__2(t)],[y__1(t), y__2(t)], singsol=all)
\[ y_{1}\relax (t ) = -{\mathrm e}^{-t} c_{1}+c_{2} {\mathrm e}^{3 t} \] \[ y_{2}\relax (t ) = {\mathrm e}^{-t} c_{1}+c_{2} {\mathrm e}^{3 t} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 46
DSolve[{y1'[t]==y1[t]+2*y2[t],y2'[t]==2*y1[t]+y2[t]},{y1[t],y2[t]},t,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(t)\to e^t (c_1 \cosh (2 t)+c_2 \sinh (2 t)) \\ \text {y2}(t)\to e^t (c_2 \cosh (2 t)+c_1 \sinh (2 t)) \\ \end{align*}