23.2.207 problem 213

Internal problem ID [5562]
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 : 213
Date solved : Tuesday, September 30, 2025 at 12:53:18 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}-a y\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.433 (sec). Leaf size: 55

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

\begin{align*} y &= 0 \\ y &= \frac {c_1 x +2 \sqrt {a \left (c_1 x +a \right )}+2 a}{c_1^{2}} \\ y &= \frac {c_1 x -2 \sqrt {a \left (c_1 x +a \right )}+2 a}{c_1^{2}} \\ \end{align*}

✓ Mathematica. Time used: 1.284 (sec). Leaf size: 68

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

\begin{align*} y(x)&\to \frac {-2 \sqrt {a (a+c_1 x)}+2 a+c_1 x}{c_1{}^2}\\ y(x)&\to \frac {2 \sqrt {a (a+c_1 x)}+2 a+c_1 x}{c_1{}^2}\\ y(x)&\to 0 \end{align*}

✗ Sympy

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

KeyError : ordered_hints