23.4.274 problem 274

Internal problem ID [6576]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 4. THE NONLINEAR EQUATION OF SECOND ORDER, page 380
Problem number : 274
Date solved : Tuesday, September 30, 2025 at 03:07:55 PM
CAS classification : [NONE]

\begin{align*} X \left (x , y\right )^{3} y^{\prime \prime }&=1 \end{align*}

✗ Maple

ode:=X(x,y(x))^3*diff(diff(y(x),x),x) = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=X[x, y[x]]^3*D[y[x],{x,2}] == 1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(X(x, y(x))**3*Derivative(y(x), (x, 2)) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solve: Cannot solve X(x, y(x))**3*Derivative(y(x), (x, 2)) - 1