2.1.9 problem 9

Internal problem ID [659]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.2. Integrals as general and particular solutions. Page 16
Problem number : 9
Date solved : Tuesday, September 30, 2025 at 04:05:04 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.025 (sec). Leaf size: 6

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

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 7

ode=D[y[x],x] == 1/(-x^2+1)^(1/2); 
ic=y[0]==0; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.096 (sec). Leaf size: 5

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

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