23.4.281 problem 284

Internal problem ID [6583]
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 : 284
Date solved : Tuesday, September 30, 2025 at 03:13:54 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} \operatorname {f5} y^{2}+\operatorname {f4} y y^{\prime }+\operatorname {f3} {y^{\prime }}^{2}+\operatorname {f2} y y^{\prime \prime }+\operatorname {f1} y^{\prime } y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.029 (sec). Leaf size: 49

ode:=f5*y(x)^2+f4*y(x)*diff(y(x),x)+f3*diff(y(x),x)^2+f2*y(x)*diff(diff(y(x),x),x)+f1*diff(y(x),x)*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 0 \\ y &= {\mathrm e}^{\int \operatorname {RootOf}\left (x +\int _{}^{\textit {\_Z}}\frac {\textit {\_f} \operatorname {f1} +\operatorname {f2}}{\textit {\_f}^{3} \operatorname {f1} +\textit {\_f}^{2} \operatorname {f2} +\textit {\_f}^{2} \operatorname {f3} +\textit {\_f} \operatorname {f4} +\operatorname {f5}}d \textit {\_f} +c_1 \right )d x +c_2} \\ \end{align*}

✗ Mathematica

ode=f5*y[x]^2 + f4*y[x]*D[y[x],x] + f3*D[y[x],x]^2 + f2*y[x]*D[y[x],{x,2}] + f1*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") 
f1 = symbols("f1") 
f2 = symbols("f2") 
f3 = symbols("f3") 
f4 = symbols("f4") 
f5 = symbols("f5") 
y = Function("y") 
ode = Eq(f1*Derivative(y(x), x)*Derivative(y(x), (x, 2)) + f2*y(x)*Derivative(y(x), (x, 2)) + f3*Derivative(y(x), x)**2 + f4*y(x)*Derivative(y(x), x) + f5*y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-f1*Derivative(y(x), (x, 2)) - f4*y(x) +