7.23.2 problem 2

Internal problem ID [588]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 5. Linear systems of differential equations. Section 5.2 (Applications). Problems at page 345
Problem number : 2
Date solved : Monday, January 27, 2025 at 02:55:05 AM
CAS classification : system_of_ODEs

\begin{align*} x^{\prime }&=x-2 y \left (t \right )\\ y^{\prime }\left (t \right )&=2 x-3 y \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 34

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

\begin{align*} x \left (t \right ) &= {\mathrm e}^{-t} \left (c_2 t +c_1 \right ) \\ y \left (t \right ) &= \frac {{\mathrm e}^{-t} \left (2 c_2 t +2 c_1 -c_2 \right )}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 46

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

\begin{align*} x(t)\to e^{-t} (2 c_1 t-2 c_2 t+c_1) \\ y(t)\to e^{-t} (2 (c_1-c_2) t+c_2) \\ \end{align*}