87.8.3 problem 3

Internal problem ID [23357]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 65
Problem number : 3
Date solved : Thursday, October 02, 2025 at 09:39:36 PM
CAS classification : [[_high_order, _missing_x], [_high_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+y y^{\prime \prime \prime \prime }&=5 \end{align*}

✗ Maple

ode:=diff(diff(y(x),x),x)+y(x)*diff(diff(diff(diff(y(x),x),x),x),x) = 5; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],{x,2}]+y[x]*D[y[x],{x,4}]==5; 
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)) - 5,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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