23.4.288 problem 291

Internal problem ID [6590]
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 : 291
Date solved : Tuesday, September 30, 2025 at 03:26:39 PM
CAS classification : [[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

\begin{align*} h \left (x \right )+g \left (y\right ) y^{\prime }+f \left (y^{\prime }\right ) y^{\prime \prime }&=0 \end{align*}

✗ Maple

ode:=h(x)+g(y(x))*diff(y(x),x)+f(diff(y(x),x))*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : multiple generators [_X0, f(_X0)] 
No algorithms are implemented to solve equat