4.19.28 $4x^2{y}^{\prime }(x{)}^2-4xy(x)y^{\prime }(x)=8x^3-y(x{)}^2$

ODE
$$4x^2{y}^{\prime }(x{)}^2-4xy(x)y^{\prime }(x)=8x^3-y(x{)}^2$$ ODE Classification

[_linear]

Book solution method
No Missing Variables ODE, Solve for $y^{\prime }$

Mathematica ✓
cpu = 0.00773566 (sec), leaf count = 42

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

Maple ✓
cpu = 0.058 (sec), leaf count = 30

$$\{y\left(x\right)=(-\sqrt{2}x+\mathit{\_}\mathit{C}\mathit{1})\sqrt{x},y\left(x\right)=(\sqrt{2}x+\mathit{\_}\mathit{C}\mathit{1})\sqrt{x}\}$$ Mathematica raw input

DSolve[-4*x*y[x]*y'[x] + 4*x^2*y'[x]^2 == 8*x^3 - y[x]^2,y[x],x]

Mathematica raw output

{{y[x] -> Sqrt[x]*(-(Sqrt[2]*x) + C[1])}, {y[x] -> Sqrt[x]*(Sqrt[2]*x + C[1])}}

Maple raw input

dsolve(4*x^2*diff(y(x),x)^2-4*x*y(x)*diff(y(x),x) = 8*x^3-y(x)^2, y(x),'implicit')

Maple raw output

y(x) = (-2^(1/2)*x+_C1)*x^(1/2), y(x) = (2^(1/2)*x+_C1)*x^(1/2)