Internal problem ID [15526]
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.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )-y \left (t \right )\\ y^{\prime }\left (t \right )&=y \left (t \right )-x \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
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[{x'[t]==x[t]-y[t],y'[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*}