##### 4.18.49 $$x^2 y'(x)^2-y(x)^4+y(x)^2=0$$

ODE
$x^2 y'(x)^2-y(x)^4+y(x)^2=0$ ODE Classiﬁcation

[_separable]

Book solution method
No Missing Variables ODE, Solve for $$y'$$

Mathematica
cpu = 0.215409 (sec), leaf count = 73

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

Maple
cpu = 0.929 (sec), leaf count = 62

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

DSolve[y[x]^2 - y[x]^4 + x^2*y'[x]^2 == 0,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(x^2*diff(y(x),x)^2+y(x)^2-y(x)^4 = 0, y(x))

Maple raw output

[y(x) = -1, y(x) = 1, y(x) = (tan(-ln(x)+_C1)^2+1)^(1/2)/tan(-ln(x)+_C1), y(x) =
 -(tan(-ln(x)+_C1)^2+1)^(1/2)/tan(-ln(x)+_C1)]