70.11.5 problem 5

Internal problem ID [18836]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.1 (Definitions and examples). Problems at page 214
Problem number : 5
Date solved : Thursday, October 02, 2025 at 03:31:24 PM
CAS classification : [[_2nd_order, _missing_x], _Van_der_Pol]

\begin{align*} y^{\prime \prime }+\mu \left (1-y^{2}\right ) y^{\prime }+y&=0 \end{align*}

✗ Maple

ode:=diff(diff(y(x),x),x)+mu*(1-y(x)^2)*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],{x,2}]+m*(1-y[x]^2)*D[y[x],x]+y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
mu = symbols("mu") 
y = Function("y") 
ode = Eq(mu*(1 - y(x)**2)*Derivative(y(x), x) + y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (y(x) + Derivative(y(x), (x, 2)))/(mu*(y(x)**2 - 1)) cannot be solved by the factorable group method