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] - Sqrt[-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*(_C1^2-4*x)^(1/2)+2*_C1)^(1/2)]