28.4.1 problem 7.1

Internal problem ID [4533]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 7. Systems of linear differential equations. Problems at page 351
Problem number : 7.1
Date solved : Monday, January 27, 2025 at 09:23:09 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )+2 x \left (t \right )-y&=0\\ x \left (t \right )+y^{\prime }-2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.258 (sec). Leaf size: 69

dsolve([diff(x(t),t)+2*x(t)-y(t)=0,x(t)+diff(y(t),t)-2*y(t)=0],singsol=all)
 

\begin{align*} x &= c_{1} {\mathrm e}^{\sqrt {3}\, t}+c_{2} {\mathrm e}^{-\sqrt {3}\, t} \\ y &= c_{1} \sqrt {3}\, {\mathrm e}^{\sqrt {3}\, t}-c_{2} \sqrt {3}\, {\mathrm e}^{-\sqrt {3}\, t}+2 c_{1} {\mathrm e}^{\sqrt {3}\, t}+2 c_{2} {\mathrm e}^{-\sqrt {3}\, t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 143

DSolve[{D[x[t],t]+2*x[t]-y[t]==0,x[t]+D[y[t],t]-2*y[t]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {1}{6} e^{-\sqrt {3} t} \left (c_1 \left (\left (3-2 \sqrt {3}\right ) e^{2 \sqrt {3} t}+3+2 \sqrt {3}\right )+\sqrt {3} c_2 \left (e^{2 \sqrt {3} t}-1\right )\right ) \\ y(t)\to \frac {1}{6} e^{-\sqrt {3} t} \left (c_2 \left (\left (3+2 \sqrt {3}\right ) e^{2 \sqrt {3} t}+3-2 \sqrt {3}\right )-\sqrt {3} c_1 \left (e^{2 \sqrt {3} t}-1\right )\right ) \\ \end{align*}