88.4.5 problem 5

Internal problem ID [23969]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 33
Problem number : 5
Date solved : Thursday, October 02, 2025 at 09:48:04 PM
CAS classification : [_separable]

\begin{align*} y^{3}+y^{\prime } \sqrt {-x^{2}+1}&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 25

ode:=y(x)^3+(-x^2+1)^(1/2)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {1}{\sqrt {c_1 +2 \arcsin \left (x \right )}} \\ y &= -\frac {1}{\sqrt {c_1 +2 \arcsin \left (x \right )}} \\ \end{align*}

✓ Mathematica. Time used: 0.207 (sec). Leaf size: 42

ode=y[x]^3+Sqrt[1-x^2]*D[y[x],{x,1}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {1}{\sqrt {2 \arcsin (x)-2 c_1}}\\ y(x)&\to \frac {1}{\sqrt {2 \arcsin (x)-2 c_1}}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.359 (sec). Leaf size: 42

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(sqrt(1 - x**2)*Derivative(y(x), x) + y(x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \frac {\sqrt {2} \sqrt {- \frac {1}{C_{1} - \operatorname {asin}{\left (x \right )}}}}{2}, \ y{\left (x \right )} = \frac {\sqrt {2} \sqrt {- \frac {1}{C_{1} - \operatorname {asin}{\left (x \right )}}}}{2}\right ] \]