Internal problem ID [31]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.4. Separable equations. Page 43
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {2 \sqrt {x}\, y^{\prime }-\sqrt {1-y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve(2*x^(1/2)*diff(y(x),x) = (1-y(x)^2)^(1/2),y(x), singsol=all)
\[ y \relax (x ) = \sin \left (\sqrt {x}+\frac {c_{1}}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.196 (sec). Leaf size: 32
DSolve[2*x^(1/2)*y'[x] == (1-y[x]^2)^(1/2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sin \left (\sqrt {x}+c_1\right ) \\ y(x)\to -1 \\ y(x)\to 1 \\ y(x)\to \text {Interval}[\{-1,1\}] \\ \end{align*}