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]