##### 4.16.17 $$y'(x)^2=a^2 y(x)^n$$

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

[_quadrature]

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

Mathematica
cpu = 0.238416 (sec), leaf count = 68

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

Maple
cpu = 0.816 (sec), leaf count = 83

$\left [y \left (x \right ) = 2^{\frac {2}{n -2}} \left (\frac {1}{a \left (\textit {\_C1} n -n x -2 \textit {\_C1} +2 x \right )}\right )^{\frac {2}{n -2}}, y \left (x \right ) = 2^{\frac {2}{n -2}} \left (\frac {1}{a \left (-\textit {\_C1} n +n x +2 \textit {\_C1} -2 x \right )}\right )^{\frac {2}{n -2}}\right ]$ Mathematica raw input

DSolve[y'[x]^2 == a^2*y[x]^n,y[x],x]

Mathematica raw output

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

Maple raw input

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

Maple raw output

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