##### 4.19.22 $$\left (a^2-x^2\right ) y'(x)^2=b^2$$

ODE
$\left (a^2-x^2\right ) y'(x)^2=b^2$ ODE Classiﬁcation

[_quadrature]

Book solution method
Missing Variables ODE, Dependent variable missing, Solve for $$y'$$

Mathematica
cpu = 0.169656 (sec), leaf count = 52

$\left \{\left \{y(x)\to -b \tan ^{-1}\left (\frac {x}{\sqrt {a^2-x^2}}\right )+c_1\right \},\left \{y(x)\to b \tan ^{-1}\left (\frac {x}{\sqrt {a^2-x^2}}\right )+c_1\right \}\right \}$

Maple
cpu = 0.07 (sec), leaf count = 44

$\left [y \left (x \right ) = b \arctan \left (\frac {x}{\sqrt {a^{2}-x^{2}}}\right )+\textit {\_C1}, y \left (x \right ) = -b \arctan \left (\frac {x}{\sqrt {a^{2}-x^{2}}}\right )+\textit {\_C1}\right ]$ Mathematica raw input

DSolve[(a^2 - x^2)*y'[x]^2 == b^2,y[x],x]

Mathematica raw output

{{y[x] -> -(b*ArcTan[x/Sqrt[a^2 - x^2]]) + C[1]}, {y[x] -> b*ArcTan[x/Sqrt[a^2 -
 x^2]] + C[1]}}

Maple raw input

dsolve((a^2-x^2)*diff(y(x),x)^2 = b^2, y(x))

Maple raw output

[y(x) = b*arctan(1/(a^2-x^2)^(1/2)*x)+_C1, y(x) = -b*arctan(1/(a^2-x^2)^(1/2)*x)
+_C1]