77.1.99 problem 126 (page 179)

Internal problem ID [17918]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 126 (page 179)
Date solved : Monday, March 31, 2025 at 04:51:25 PM
CAS classification : [[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]]

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

✓ Maple. Time used: 0.032 (sec). Leaf size: 36

ode:=5*diff(diff(diff(y(x),x),x),x)^2-3*diff(diff(y(x),x),x)*diff(diff(diff(diff(y(x),x),x),x),x) = 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: 0.206 (sec). Leaf size: 28

ode=5*D[y[x],{x,3}]^2-3*D[y[x],{x,2}]*D[y[x],{x,4}]==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