60.8.14 problem 1850

Internal problem ID [11775]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 7, non-linear third and higher order
Problem number : 1850
Date solved : Sunday, March 30, 2025 at 09:15:01 PM
CAS classification : [[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],x]^3*Derivative[3][y][x] - D[y[x],{x,2}]*Derivative[3][y][x] + D[y[x],x]*Derivative[4][y][x] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x)**3*Derivative(y(x), (x, 3)) + Derivative(y(x), x)*Derivative(y(x), (x, 4)) - Derivative(y(x), (x, 2))*Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE (sqrt(729*Derivative(y(x), (x, 2))**2 + 108*Derivative(y(x), (x, 4))**3/Derivative(y(x), (x, 3))**3)/2 - 27*Derivative(y(x), (x, 2))/2)**(1/3)/3 + Derivative(y(x), x) - Derivative(y(x), (x, 4))/((sqrt(729*Derivative(y(x), (x, 2))**2 + 108*Derivative(y(x), (x, 4))**3/Derivative(y(x), (x, 3))**3)/2 - 27*Derivative(y(x), (x, 2))/2)**(1/3)*Derivative(y(x), (x, 3))) cannot be solved by the factorable group method