77.1.85 problem 112 (page 172)

Internal problem ID [17904]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 112 (page 172)
Date solved : Monday, March 31, 2025 at 04:49:40 PM
CAS classification : [[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]]

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

✗ Maple

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

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 32

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

\[ y(x)\to \frac {c_1 x^3}{6}-\frac {c_1{}^3 x^2}{2}+c_3 x+c_2 \]

✗ Sympy

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

Timed Out