##### 4.15.17 $$x \left (1-x^2 y(x)^4\right ) y'(x)+y(x)=0$$

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

[[_homogeneous, class G], _rational]

Book solution method
Exact equation, integrating factor

Mathematica
cpu = 0.29615 (sec), leaf count = 139

$\left \{\left \{y(x)\to -\sqrt {c_1-\frac {\sqrt {x^2 \left (-1+c_1{}^2 x^2\right )}}{x^2}}\right \},\left \{y(x)\to \sqrt {c_1-\frac {\sqrt {x^2 \left (-1+c_1{}^2 x^2\right )}}{x^2}}\right \},\left \{y(x)\to -\sqrt {\frac {\sqrt {x^2 \left (-1+c_1{}^2 x^2\right )}}{x^2}+c_1}\right \},\left \{y(x)\to \sqrt {\frac {\sqrt {x^2 \left (-1+c_1{}^2 x^2\right )}}{x^2}+c_1}\right \}\right \}$

Maple
cpu = 0.119 (sec), leaf count = 129

$\left [y \left (x \right ) = -\frac {\sqrt {-2 x \textit {\_C1} \left (-x +\sqrt {-4 \textit {\_C1}^{2}+x^{2}}\right )}}{2 x \textit {\_C1}}, y \left (x \right ) = \frac {\sqrt {-2 x \textit {\_C1} \left (-x +\sqrt {-4 \textit {\_C1}^{2}+x^{2}}\right )}}{2 x \textit {\_C1}}, y \left (x \right ) = -\frac {\sqrt {2}\, \sqrt {x \textit {\_C1} \left (x +\sqrt {-4 \textit {\_C1}^{2}+x^{2}}\right )}}{2 x \textit {\_C1}}, y \left (x \right ) = \frac {\sqrt {2}\, \sqrt {x \textit {\_C1} \left (x +\sqrt {-4 \textit {\_C1}^{2}+x^{2}}\right )}}{2 x \textit {\_C1}}\right ]$ Mathematica raw input

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

Mathematica raw output

{{y[x] -> -Sqrt[C[1] - Sqrt[x^2*(-1 + x^2*C[1]^2)]/x^2]}, {y[x] -> Sqrt[C[1] - S
qrt[x^2*(-1 + x^2*C[1]^2)]/x^2]}, {y[x] -> -Sqrt[C[1] + Sqrt[x^2*(-1 + x^2*C[1]^
2)]/x^2]}, {y[x] -> Sqrt[C[1] + Sqrt[x^2*(-1 + x^2*C[1]^2)]/x^2]}}

Maple raw input

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

Maple raw output

[y(x) = -1/2/x/_C1*(-2*x*_C1*(-x+(-4*_C1^2+x^2)^(1/2)))^(1/2), y(x) = 1/2/x/_C1*
(-2*x*_C1*(-x+(-4*_C1^2+x^2)^(1/2)))^(1/2), y(x) = -1/2/x/_C1*2^(1/2)*(x*_C1*(x+
(-4*_C1^2+x^2)^(1/2)))^(1/2), y(x) = 1/2/x/_C1*2^(1/2)*(x*_C1*(x+(-4*_C1^2+x^2)^
(1/2)))^(1/2)]