4.19.28 \(4 x^2 y'(x)^2-4 x y(x) y'(x)=8 x^3-y(x)^2\)

ODE
\[ 4 x^2 y'(x)^2-4 x y(x) y'(x)=8 x^3-y(x)^2 \] ODE Classification

[_linear]

Book solution method
No Missing Variables ODE, Solve for \(y'\)

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

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

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

\[ \left \{ y \relax (x ) = \left (-\sqrt {2}x+{\it \_C1} \right ) \sqrt {x},y \relax (x ) = \left (\sqrt {2}x+{\it \_C1} \right ) \sqrt {x} \right \} \] 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)