Rayleigh Differential Equation

Author

Eric W. Weisstein
February 27, 2005

This notebook downloaded from http://mathworld.wolfram.com/notebooks/DifferentialEquations/RayleighDifferentialEquation.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/RayleighDifferentialEquation.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Exact Solution

DSolve[y''[x]-μ(1-(1/3)((y'[x])^2))y'[x]+y[x]==0,y[x],x]

Relationship to van der Pol Equation

eqn1=FullSimplify[D[y''[x]-μ(1-(1/3)((y'[x])^2))y'[x]+y[x],x]/.Derivative[n_][y][x]:>Derivative[n-1][y][x]]

eqn2=y''[x]-μ(1-((y[x])^2))y'[x]+y[x];

Simplify[eqn1-eqn2]