60.1.61 problem 62

Internal problem ID [10075]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 62
Date solved : Sunday, March 30, 2025 at 03:03:25 PM
CAS classification : [NONE]

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

✓ Maple. Time used: 0.123 (sec). Leaf size: 34

ode:=diff(y(x),x)-(y(x)-x^2*(x^2-y(x)^2)^(1/2))/(x*y(x)*(x^2-y(x)^2)^(1/2)+x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {y^{2}}{2}+\arctan \left (\frac {y}{\sqrt {x^{2}-y^{2}}}\right )+\frac {x^{2}}{2}-c_1 = 0 \]

✓ Mathematica. Time used: 1.598 (sec). Leaf size: 44

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

\[ \text {Solve}\left [-\arctan \left (\frac {\sqrt {x^2-y(x)^2}}{y(x)}\right )+\frac {x^2}{2}+\frac {y(x)^2}{2}=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out