71.3.22 problem 17

Internal problem ID [14293]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.1, page 40
Problem number : 17
Date solved : Wednesday, March 05, 2025 at 10:43:01 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{\prime }&=\frac {1}{\sqrt {15-x^{2}-y^{2}}} \end{align*}

✗ Maple

ode:=diff(y(x),x) = 1/(15-x^2-y(x)^2)^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],x]==1/Sqrt[15-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(Derivative(y(x), x) - 1/sqrt(-x**2 - y(x)**2 + 15),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out