Internal problem ID [3644]
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]
\[ \boxed {y^{\prime } \sqrt {-x^{2}+1}-y^{2}=1} \]
✓ 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: 0.283 (sec). Leaf size: 47
DSolve[y'[x] Sqrt[1-x^2]==1+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\tan \left (2 \arctan \left (\frac {\sqrt {1-x^2}}{x+1}\right )-c_1\right ) y(x)\to -i y(x)\to i \end{align*}