23.6.13 problem 13

Internal problem ID [6812]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 6. THE EQUATION IS NONLINEAR AND OF ORDER GREATER THAN TWO, page 427
Problem number : 13
Date solved : Tuesday, September 30, 2025 at 03:51:58 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime } y^{\prime \prime }&=a x {y^{\prime }}^{5}+3 {y^{\prime \prime }}^{2} \end{align*}

✗ Maple

ode:=diff(y(x),x)*diff(diff(y(x),x),x) = a*x*diff(y(x),x)^5+3*diff(diff(y(x),x),x)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],x]*D[y[x],{x,2}] == a*x*D[y[x],x]^5 + 3*D[y[x],{x,2}]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(-a*x*Derivative(y(x), x)**5 + Derivative(y(x), x)*Derivative(y(x), (x, 2)) - 3*Derivative(y(x), (x, 2))**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out