4.19.43 $x^6{y}^{\prime }(x{)}^2-2x{y}^{\prime }(x)-4y(x)=0$

ODE
$$x^6{y}^{\prime }(x{)}^2-2x{y}^{\prime }(x)-4y(x)=0$$ ODE Classification

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

Book solution method
No Missing Variables ODE, Solve for $y$

Mathematica ✓
cpu = 0.385876 (sec), leaf count = 120

$$\{\text{Solve}[4c_1+\frac{2\sqrt{4x^{6}y(x)+x^2}{\tanh }^{-1}\left(\sqrt{4x^{4}y(x)+1}\right)}{x\sqrt{4x^{4}y(x)+1}}+\log (y(x))=0,y(x)],\text{Solve}[4c_1+\log (y(x))=\frac{2\sqrt{4x^{6}y(x)+x^2}{\tanh }^{-1}\left(\sqrt{4x^{4}y(x)+1}\right)}{x\sqrt{4x^{4}y(x)+1}},y(x)]\}$$

Maple ✓
cpu = 0.063 (sec), leaf count = 71

$$\{\ln \left(x\right)-\mathit{\_}\mathit{C}\mathit{1}-\frac{\ln \left(x^{4}y\left(x\right)\right)}{4}-\frac{1}{2}\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\sqrt{4x^{4}y\left(x\right)+1}\right)=0,\ln \left(x\right)-\mathit{\_}\mathit{C}\mathit{1}-\frac{\ln \left(x^{4}y\left(x\right)\right)}{4}+\frac{1}{2}\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\sqrt{4x^{4}y\left(x\right)+1}\right)=0,y\left(x\right)=-\frac{1}{4x^4}\}$$ Mathematica raw input

DSolve[-4*y[x] - 2*x*y'[x] + x^6*y'[x]^2 == 0,y[x],x]

Mathematica raw output

{Solve[4*C[1] + Log[y[x]] + (2*ArcTanh[Sqrt[1 + 4*x^4*y[x]]]*Sqrt[x^2 + 4*x^6*y[
x]])/(x*Sqrt[1 + 4*x^4*y[x]]) == 0, y[x]], Solve[4*C[1] + Log[y[x]] == (2*ArcTan
h[Sqrt[1 + 4*x^4*y[x]]]*Sqrt[x^2 + 4*x^6*y[x]])/(x*Sqrt[1 + 4*x^4*y[x]]), y[x]]}

Maple raw input

dsolve(x^6*diff(y(x),x)^2-2*x*diff(y(x),x)-4*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = -1/4/x^4, ln(x)-_C1-1/4*ln(x^4*y(x))-1/2*arctanh((4*x^4*y(x)+1)^(1/2)) = 
0, ln(x)-_C1-1/4*ln(x^4*y(x))+1/2*arctanh((4*x^4*y(x)+1)^(1/2)) = 0