66.2.40 problem Problem 55

Internal problem ID [13868]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER. Problems page 172
Problem number : Problem 55
Date solved : Monday, March 31, 2025 at 08:15:38 AM
CAS classification : [[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]]

\begin{align*} 6 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2}&=0 \end{align*}

✓ Maple. Time used: 0.030 (sec). Leaf size: 25

ode:=6*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 &= \frac {\left (x +c_2 \right )^{8} c_1}{2612736}+c_3 x +c_4 \\ \end{align*}

✓ Mathematica. Time used: 0.151 (sec). Leaf size: 26

ode=6*D[y[x],{x,2}]*D[y[x],{x,4}]-5*D[y[x],{x,3}]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{56} c_2 (x-6 c_1){}^8+c_4 x+c_3 \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*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(30)*sqrt(Dummy_85(x)*Derivative(Dummy_85(x), (x, 2)))/5 + Derivative(Dummy_85(x), x) cannot be solved by the factorable group method