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 = 0.208372 (sec), leaf count = 42
\[\left \{\left \{y(x)\to \sqrt {x} \left (-\sqrt {2} x+c_1\right )\right \},\left \{y(x)\to \sqrt {x} \left (\sqrt {2} x+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.093 (sec), leaf count = 30
\[\left [y \left (x \right ) = \left (-\sqrt {2}\, x +\textit {\_C1} \right ) \sqrt {x}, y \left (x \right ) = \left (\sqrt {2}\, x +\textit {\_C1} \right ) \sqrt {x}\right ]\] 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))
Maple raw output
[y(x) = (-2^(1/2)*x+_C1)*x^(1/2), y(x) = (2^(1/2)*x+_C1)*x^(1/2)]