##### 4.19.3 $$-x^4+x^2 y'(x)^2+\left (1-x^2\right ) y(x)^2-2 x y(x) y'(x)=0$$

ODE
$-x^4+x^2 y'(x)^2+\left (1-x^2\right ) y(x)^2-2 x y(x) y'(x)=0$ ODE Classiﬁcation

[_rational, [_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]]

Book solution method
Change of variable

Mathematica
cpu = 0.243495 (sec), leaf count = 26

$\{\{y(x)\to -x \sinh (x-c_1)\},\{y(x)\to x \sinh (x+c_1)\}\}$

Maple
cpu = 16.045 (sec), leaf count = 59

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

DSolve[-x^4 + (1 - x^2)*y[x]^2 - 2*x*y[x]*y'[x] + x^2*y'[x]^2 == 0,y[x],x]

Mathematica raw output

{{y[x] -> -(x*Sinh[x - C[1]])}, {y[x] -> x*Sinh[x + C[1]]}}

Maple raw input

dsolve(x^2*diff(y(x),x)^2-2*x*y(x)*diff(y(x),x)-x^4+(-x^2+1)*y(x)^2 = 0, y(x))

Maple raw output

[y(x) = -I*x, y(x) = I*x, y(x) = -1/2*x*(exp(x)^2/_C1^2-1)/exp(x)*_C1, y(x) = 1/
2*x*(exp(x)^2*_C1^2-1)/exp(x)/_C1]