4.15.12 $2(x-y(x{)}^4)y^{\prime }(x)=y(x)$

ODE
$$2(x-y(x{)}^4)y^{\prime }(x)=y(x)$$ ODE Classification

[[_homogeneous, `class G`], _rational]

Book solution method
Exact equation, integrating factor

Mathematica ✓
cpu = 0.0126665 (sec), leaf count = 123

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

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

$$\{{\left(y\left(x\right)\right)}^4-{\left(y\left(x\right)\right)}^2\mathit{\_}\mathit{C}\mathit{1}+x=0\}$$ 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