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 = 0.0126665 (sec), leaf count = 123

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

Maple
cpu = 0.006 (sec), leaf count = 16

\[ \left \{ \left (y \relax (x ) \right ) ^{4}- \left (y \relax (x ) \right ) ^{2}{\it \_C1}+x=0 \right \} \] 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),'implicit')

Maple raw output

y(x)^4-y(x)^2*_C1+x = 0