23.2.224 problem 230

Internal problem ID [5579]
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 : 230
Date solved : Tuesday, September 30, 2025 at 01:00:27 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(y)]`]]

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

✓ Maple. Time used: 0.796 (sec). Leaf size: 57

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

\begin{align*} y &= \sqrt {-x^{2}+a} \\ y &= -\sqrt {-x^{2}+a} \\ y &= \sqrt {c_1^{2}-2 c_1 x +a} \\ y &= -\sqrt {c_1^{2}-2 c_1 x +a} \\ \end{align*}

✓ Mathematica. Time used: 0.341 (sec). Leaf size: 61

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

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

✗ Sympy

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

Timed Out