23.4.234 problem 234

Internal problem ID [6536]
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 : 234
Date solved : Tuesday, September 30, 2025 at 03:02:49 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \operatorname {f3} \left (x \right ) y^{2}+\operatorname {f2} \left (x \right ) y y^{\prime }+\operatorname {f1} \left (x \right ) {y^{\prime }}^{2}+\operatorname {f0} \left (x \right ) y y^{\prime \prime }&=0 \end{align*}

✗ Maple

ode:=f3(x)*y(x)^2+f2(x)*y(x)*diff(y(x),x)+f1(x)*diff(y(x),x)^2+f0(x)*y(x)*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=f3[x]*y[x]^2 + f2[x]*y[x]*D[y[x],x] + f1[x]*D[y[x],x]^2 + f0[x]*y[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(f0(x)*y(x)*Derivative(y(x), (x, 2)) + f1(x)*Derivative(y(x), x)**2 + f2(x)*y(x)*Derivative(y(x), x) + f3(x)*y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -(sqrt((-4*f0(x)*f1(x)*Derivative(y(x), (x, 2)) - 4*f1(x)*f3(x)*