12.21.1 problem section 10.4, problem 1

Internal problem ID [2239]
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
Date solved : Monday, January 27, 2025 at 05:43:58 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}y_{1} \left (t \right )&=y_{1} \left (t \right )+2 y_{2} \left (t \right )\\ \frac {d}{d t}y_{2} \left (t \right )&=2 y_{1} \left (t \right )+y_{2} \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 34

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)],singsol=all)
 

\begin{align*} y_{1} \left (t \right ) &= c_1 \,{\mathrm e}^{3 t}+c_2 \,{\mathrm e}^{-t} \\ y_{2} \left (t \right ) &= c_1 \,{\mathrm e}^{3 t}-c_2 \,{\mathrm e}^{-t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 68

DSolve[{D[ y1[t],t]==y1[t]+2*y2[t],D[ y2[t],t]==2*y1[t]+y2[t]},{y1[t],y2[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} \text {y1}(t)\to \frac {1}{2} e^{-t} \left (c_1 \left (e^{4 t}+1\right )+c_2 \left (e^{4 t}-1\right )\right ) \\ \text {y2}(t)\to \frac {1}{2} e^{-t} \left (c_1 \left (e^{4 t}-1\right )+c_2 \left (e^{4 t}+1\right )\right ) \\ \end{align*}