56.1.19 problem 19

Internal problem ID [8731]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 19
Date solved : Sunday, March 30, 2025 at 01:28:22 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{\prime }&=\sqrt {1-x^{2}-y^{2}} \end{align*}

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],x]==Sqrt[ 1-x^2-y[x]^2]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-sqrt(-x**2 - y(x)**2 + 1) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -sqrt(-x**2 - y(x)**2 + 1) + Derivative(y(x), x) cannot be solved by the lie group method