28.4.3 problem 7.3

Internal problem ID [4535]
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 : 7.3
Date solved : Monday, January 27, 2025 at 09:23:11 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }\left (t \right )-x \left (t \right )+3 y&=0\\ 3 x \left (t \right )-y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.031 (sec). Leaf size: 40

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

\begin{align*} x &= {\mathrm e}^{t} \left (\sin \left (3 t \right ) c_{1} +\cos \left (3 t \right ) c_{2} \right ) \\ y &= {\mathrm e}^{t} \left (-\cos \left (3 t \right ) c_{1} +\sin \left (3 t \right ) c_{2} \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 47

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

\begin{align*} x(t)\to e^t (c_1 \cos (3 t)-c_2 \sin (3 t)) \\ y(t)\to e^t (c_2 \cos (3 t)+c_1 \sin (3 t)) \\ \end{align*}