ODE
\[ \sqrt {1-x^2} y'(x)=y(x)^2+1 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.30269 (sec), leaf count = 11
\[\left \{\left \{y(x)\to \tan \left (\sin ^{-1}(x)+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.031 (sec), leaf count = 9
\[[y \left (x \right ) = \tan \left (\arcsin \left (x \right )+\textit {\_C1} \right )]\] Mathematica raw input
DSolve[Sqrt[1 - x^2]*y'[x] == 1 + y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> Tan[ArcSin[x] + C[1]]}}
Maple raw input
dsolve(diff(y(x),x)*(-x^2+1)^(1/2) = 1+y(x)^2, y(x))
Maple raw output
[y(x) = tan(arcsin(x)+_C1)]