Internal problem ID [3135]
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]
\[ \boxed {y^{\prime } \sqrt {1-x^{2}}-1-y^{2}=0} \]
✓ 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)
\[ y \left (x \right ) = \tan \left (\arcsin \left (x \right )+c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.256 (sec). Leaf size: 45
DSolve[y'[x] Sqrt[1-x^2]==1+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\tan \left (2 \cot ^{-1}\left (\frac {x+1}{\sqrt {1-x^2}}\right )-c_1\right ) \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}