Internal problem ID [6375]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 83.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-\sqrt {1-y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 8
dsolve(diff(y(x),x)=sqrt(1-y(x)^2),y(x), singsol=all)
\[ y \relax (x ) = \sin \left (c_{1}+x \right ) \]
✓ Solution by Mathematica
Time used: 2.385 (sec). Leaf size: 54
DSolve[y'[x]==Sqrt[1-y[x]^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\tan (x+c_1)}{\sqrt {\sec ^2(x+c_1)}} \\ y(x)\to \frac {\tan (x+c_1)}{\sqrt {\sec ^2(x+c_1)}} \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}