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]
\[ \boxed {y^{\prime }=\frac {1}{\sqrt {-x^{2}+1}}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 6
dsolve([diff(y(x),x) = 1/(-x^2+1)^(1/2),y(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \arcsin \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 31
DSolve[{y'[x] == 1/(-x^2+1)^(1/2),y[0]==0},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \left (\pi -4 \arctan \left (\frac {\sqrt {1-x^2}}{x+1}\right )\right ) \]