##### 4.20.24 $$y(x)^2 y'(x)^2=a^2$$

ODE
$y(x)^2 y'(x)^2=a^2$ ODE Classiﬁcation

[_quadrature]

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

Mathematica
cpu = 0.176021 (sec), leaf count = 85

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

Maple
cpu = 0.029 (sec), leaf count = 49

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

DSolve[y[x]^2*y'[x]^2 == a^2,y[x],x]

Mathematica raw output

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

Maple raw input

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

Maple raw output

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