##### 4.14.27 $$\left (1-x^4 y(x)^2\right ) y'(x)=x^3 y(x)^3$$

ODE
$\left (1-x^4 y(x)^2\right ) y'(x)=x^3 y(x)^3$ ODE Classiﬁcation

[[_homogeneous, class G], _rational]

Book solution method
Exact equation, integrating factor

Mathematica
cpu = 0.342498 (sec), leaf count = 117

$\left \{\left \{y(x)\to -\sqrt {\frac {1-\sqrt {1+4 c_1 x^4}}{x^4}}\right \},\left \{y(x)\to \sqrt {\frac {1-\sqrt {1+4 c_1 x^4}}{x^4}}\right \},\left \{y(x)\to -\sqrt {\frac {1+\sqrt {1+4 c_1 x^4}}{x^4}}\right \},\left \{y(x)\to \sqrt {\frac {1+\sqrt {1+4 c_1 x^4}}{x^4}}\right \}\right \}$

Maple
cpu = 0.312 (sec), leaf count = 191

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

DSolve[(1 - x^4*y[x]^2)*y'[x] == x^3*y[x]^3,y[x],x]

Mathematica raw output

{{y[x] -> -Sqrt[(1 - Sqrt[1 + 4*x^4*C[1]])/x^4]}, {y[x] -> Sqrt[(1 - Sqrt[1 + 4*
x^4*C[1]])/x^4]}, {y[x] -> -Sqrt[(1 + Sqrt[1 + 4*x^4*C[1]])/x^4]}, {y[x] -> Sqrt
[(1 + Sqrt[1 + 4*x^4*C[1]])/x^4]}}

Maple raw input

dsolve((1-x^4*y(x)^2)*diff(y(x),x) = x^3*y(x)^3, y(x))

Maple raw output

[y(x) = (-_C1-(_C1*x^4+_C1^2)^(1/2))^(1/2)*(1/_C1*(-_C1-(_C1*x^4+_C1^2)^(1/2))+2
)/x^4, y(x) = (-_C1+(_C1*x^4+_C1^2)^(1/2))^(1/2)*((-_C1+(_C1*x^4+_C1^2)^(1/2))/_
C1+2)/x^4, y(x) = -(-_C1-(_C1*x^4+_C1^2)^(1/2))^(1/2)*(1/_C1*(-_C1-(_C1*x^4+_C1^
2)^(1/2))+2)/x^4, y(x) = -(-_C1+(_C1*x^4+_C1^2)^(1/2))^(1/2)*((-_C1+(_C1*x^4+_C1
^2)^(1/2))/_C1+2)/x^4]