28.4.2 problem 7.2

Internal problem ID [4534]
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 : 7.2
Date solved : Monday, January 27, 2025 at 09:23:10 AM
CAS classification : system_of_ODEs

\begin{align*} 2 x^{\prime }\left (t \right )+x \left (t \right )-5 y^{\prime }-4 y&=0\\ -y^{\prime }-2 x \left (t \right )+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.039 (sec). Leaf size: 34

dsolve([2*diff(x(t),t)+x(t)-5*diff(y(t),t)-4*y(t)=0,3*diff(y(t),t)-2*x(t)-4*diff(y(t),t)+y(t)=0],singsol=all)
 

\begin{align*} x &= {\mathrm e}^{-\frac {7 t}{2}} c_{1} +c_{2} {\mathrm e}^{-t} \\ y &= \frac {4 \,{\mathrm e}^{-\frac {7 t}{2}} c_{1}}{9}+c_{2} {\mathrm e}^{-t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 86

DSolve[{2*D[x[t],t]+x[t]-5*D[y[t],t]-4*y[t]==0,3*D[y[t],t]-2*x[t]-4*D[y[t],t]+y[t]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {1}{5} e^{-7 t/2} \left (c_1 \left (9-4 e^{5 t/2}\right )+9 c_2 \left (e^{5 t/2}-1\right )\right ) \\ y(t)\to \frac {1}{5} e^{-7 t/2} \left (c_2 \left (9 e^{5 t/2}-4\right )-4 c_1 \left (e^{5 t/2}-1\right )\right ) \\ \end{align*}