Internal problem ID [3136]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 14
Problem number: 390.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } \sqrt {1-x^{2}}-1-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 9
dsolve(diff(y(x),x)*sqrt(-x^2+1) = 1+y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \tan \left (\arcsin \relax (x )+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.235 (sec). Leaf size: 25
DSolve[y'[x] Sqrt[1-x^2]==1+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \tan (\text {ArcSin}(x)+c_1) \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}