88.3.1 problem 1

Internal problem ID [23955]
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 1. Introduction. Exercise at page 22
Problem number : 1
Date solved : Thursday, October 02, 2025 at 09:47:40 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 8

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

\[ y = \arcsin \left (x \right )+c_1 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 10

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

\begin{align*} y(x)&\to \arcsin (x)+c_1 \end{align*}

✓ Sympy. Time used: 0.117 (sec). Leaf size: 7

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

\[ y{\left (x \right )} = C_{1} + \operatorname {asin}{\left (x \right )} \]