75.29.2 problem 803

Internal problem ID [17256]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 3 (Systems of differential equations). Section 22. Integration of homogeneous linear systems with constant coefficients. Eulers method. Exercises page 230
Problem number : 803
Date solved : Tuesday, January 28, 2025 at 09:58:29 AM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 60

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

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