72.9.1 problem 1

Internal problem ID [14797]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 3. Linear Systems. Exercises section 3.1. page 258
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 07:15:52 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.056 (sec). Leaf size: 20

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

\begin{align*} x \left (t \right ) &= c_{1} t +c_{2} \\ y &= c_{1} t -c_{1} +c_{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 32

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

\begin{align*} x(t)\to c_1 (t+1)-c_2 t \\ y(t)\to (c_1-c_2) t+c_2 \\ \end{align*}