67.2.5 problem Problem 1(e)

Internal problem ID [13891]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 1(e)
Date solved : Monday, March 31, 2025 at 08:16:34 AM
CAS classification : [[_high_order, _missing_x], [_high_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+y y^{\prime \prime \prime \prime }&=1 \end{align*}

✗ Maple

ode:=diff(diff(y(x),x),x)+y(x)*diff(diff(diff(diff(y(x),x),x),x),x) = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],{x,2}]+y[x]*D[y[x],{x,4}]==1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)*Derivative(y(x), (x, 4)) + Derivative(y(x), (x, 2)) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solve: Cannot solve y(x)*Derivative(y(x), (x, 4)) + Derivative(y(x), (x, 2)) - 1