##### 4.15.12 $$2 \left (x-y(x)^4\right ) y'(x)=y(x)$$

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

[[_homogeneous, class G], _rational]

Book solution method
Exact equation, integrating factor

Mathematica
cpu = 0.350689 (sec), leaf count = 123

$\left \{\left \{y(x)\to -\frac {\sqrt {c_1-\sqrt {-4 x+c_1{}^2}}}{\sqrt {2}}\right \},\left \{y(x)\to \frac {\sqrt {c_1-\sqrt {-4 x+c_1{}^2}}}{\sqrt {2}}\right \},\left \{y(x)\to -\frac {\sqrt {\sqrt {-4 x+c_1{}^2}+c_1}}{\sqrt {2}}\right \},\left \{y(x)\to \frac {\sqrt {\sqrt {-4 x+c_1{}^2}+c_1}}{\sqrt {2}}\right \}\right \}$

Maple
cpu = 0.044 (sec), leaf count = 89

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

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

Mathematica raw output

{{y[x] -> -(Sqrt[C[1] - Sqrt[-4*x + C[1]^2]]/Sqrt[2])}, {y[x] -> Sqrt[C[1] - Sqr
t[-4*x + C[1]^2]]/Sqrt[2]}, {y[x] -> -(Sqrt[C[1] + Sqrt[-4*x + C[1]^2]]/Sqrt[2])
}, {y[x] -> Sqrt[C[1] + Sqrt[-4*x + C[1]^2]]/Sqrt[2]}}

Maple raw input

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

Maple raw output

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