4.8.43 \(\sqrt {1-x^2} y'(x)=y(x)^2+1\)

ODE
\[ \sqrt {1-x^2} y'(x)=y(x)^2+1 \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.0197276 (sec), leaf count = 11

\[\left \{\left \{y(x)\to \tan \left (c_1+\sin ^{-1}(x)\right )\right \}\right \}\]

Maple
cpu = 0.01 (sec), leaf count = 12

\[ \left \{ \arcsin \relax (x ) -\arctan \left (y \relax (x ) \right ) +{\it \_C1}=0 \right \} \] 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),'implicit')

Maple raw output

arcsin(x)-arctan(y(x))+_C1 = 0