60.8.15 problem 1852

Internal problem ID [11776]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 7, non-linear third and higher order
Problem number : 1852
Date solved : Sunday, March 30, 2025 at 09:15:02 PM
CAS classification : [[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]]

\begin{align*} 3 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2}&=0 \end{align*}

✓ Maple. Time used: 0.089 (sec). Leaf size: 36

ode:=3*diff(diff(y(x),x),x)*diff(diff(diff(diff(y(x),x),x),x),x)-5*diff(diff(diff(y(x),x),x),x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= c_1 x +c_2 \\ y &= 3 \left (x +c_2 \right ) \sqrt {6}\, c_1 \sqrt {-\frac {c_1}{x +c_2}}+c_3 x +c_4 \\ \end{align*}

✓ Mathematica. Time used: 0.211 (sec). Leaf size: 28

ode=-5*Derivative[3][y][x]^2 + 3*D[y[x],{x,2}]*Derivative[4][y][x] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_2 \left (-\sqrt {2 x+3 c_1}\right )+c_4 x+c_3 \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*Derivative(y(x), (x, 2))*Derivative(y(x), (x, 4)) - 5*Derivative(y(x), (x, 3))**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -sqrt(15)*sqrt(Dummy_85(x)*Derivative(Dummy_85(x), (x, 2)))/5 + Derivative(Dummy_85(x), x) cannot be solved by the factorable group method