23.2.212 problem 218

Internal problem ID [5567]
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 : 218
Date solved : Tuesday, September 30, 2025 at 12:53:23 PM
CAS classification : [_rational]

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

✓ Maple. Time used: 0.379 (sec). Leaf size: 952

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

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

✓ Mathematica. Time used: 0.25 (sec). Leaf size: 112

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

\begin{align*} y(x)&\to \sqrt {c_1 \left (x^2+\frac {a}{1+c_1}\right )}\\ y(x)&\to -\sqrt {\left (\sqrt {a}-i x\right )^2}\\ y(x)&\to \sqrt {\left (\sqrt {a}-i x\right )^2}\\ y(x)&\to -\sqrt {\left (\sqrt {a}+i x\right )^2}\\ y(x)&\to \sqrt {\left (\sqrt {a}+i x\right )^2} \end{align*}

✗ Sympy

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

Timed Out