8.1.9 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 : Monday, January 27, 2025 at 02:56:48 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*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 6

dsolve([diff(y(x),x) = 1/(-x^2+1)^(1/2),y(0) = 0],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 7

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

\[ y(x)\to \arcsin (x) \]