16.1.3 problem 2(c)

Internal problem ID [3405]
Book : Elementary Differential Equations, Martin, Reissner, 2nd ed, 1961
Section : Exercis 2, page 5
Problem number : 2(c)
Date solved : Monday, January 27, 2025 at 07:35:51 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

dsolve(diff(y(x),x)=2/sqrt(1-x^2),y(x), singsol=all)
 

\[ y \left (x \right ) = 2 \arcsin \left (x \right )+c_{1} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 12

DSolve[D[y[x],x]==2/Sqrt[1-x^2],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2 \arcsin (x)+c_1 \]