23.2.86 problem 88

Internal problem ID [5441]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 88
Date solved : Tuesday, September 30, 2025 at 12:43:24 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

\begin{align*} 3 {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.029 (sec). Leaf size: 603

ode:=3*diff(y(x),x)^2-2*x*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 60.098 (sec). Leaf size: 995

ode=3 (D[y[x],x])^2-2 x D[y[x],x]+y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

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

NotImplementedError : The given ODE -x/3 - sqrt(x**2 - 3*y(x))/3 + Derivative(y(x), x) cannot be solved by the factorable group method