Internal problem ID [9]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {1}{\sqrt {-x^{2}+1}}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 6
dsolve([diff(y(x),x) = 1/(-x^2+1)^(1/2),y(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = \arcsin \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 19
DSolve[{y'[x] == 1/(-x^2+1)^(1/2),y[0]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \operatorname {ArcTan}\left (\frac {x}{\sqrt {1-x^2}}\right ) \\ \end{align*}