29.31.23 problem 922

Internal problem ID [5502]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 31
Problem number : 922
Date solved : Sunday, March 30, 2025 at 08:25:59 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

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

✓ Maple. Time used: 0.180 (sec). Leaf size: 84

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

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

✓ Mathematica. Time used: 0.394 (sec). Leaf size: 100

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

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

✗ Sympy

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

Timed Out