76.11.2 problem 2

Internal problem ID [17475]
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 : 2
Date solved : Monday, March 31, 2025 at 04:14:36 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+y^{\prime }+y+y^{3}&=0 \end{align*}

✗ Maple

ode:=diff(diff(y(t),t),t)+diff(y(t),t)+y(t)+y(t)^3 = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[t],{t,2}]+D[y[t],t]+y[t]+y[t]^3==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t)**3 + y(t) + Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : solve: Cannot solve y(t)**3 + y(t) + Derivative(y(t), t) + Derivative(y(t), (t, 2))