23.2.245 problem 251

Internal problem ID [5600]
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 : 251
Date solved : Saturday, October 04, 2025 at 04:39:14 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(y)]`]]

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

✓ Maple. Time used: 0.263 (sec). Leaf size: 766

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

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

✓ Mathematica. Time used: 0.855 (sec). Leaf size: 86

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

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

✗ Sympy

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

Timed Out