##### 4.19.23 $$\left (a^2-x^2\right ) y'(x)^2=x^2$$

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

[_quadrature]

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

Mathematica
cpu = 0.164382 (sec), leaf count = 43

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

Maple
cpu = 0.071 (sec), leaf count = 52

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

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

Mathematica raw output

{{y[x] -> -Sqrt[a^2 - x^2] + C[1]}, {y[x] -> Sqrt[a^2 - x^2] + C[1]}}

Maple raw input

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

Maple raw output

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