ODE
\[ 12 x^3+x y'(x)^4-2 y(x) y'(x)^3=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries]]
Book solution method
No Missing Variables ODE, Solve for \(y\)
Mathematica ✓
cpu = 144.879 (sec), leaf count = 1
\[\text {$\$$Aborted}\]
Maple ✓
cpu = 3.263 (sec), leaf count = 62
\[\left [y \left (x \right ) = -\frac {2 \sqrt {6}\, x^{\frac {3}{2}}}{3}, y \left (x \right ) = \frac {2 \sqrt {6}\, x^{\frac {3}{2}}}{3}, y \left (x \right ) = -\frac {2 \sqrt {-6 x}\, x}{3}, y \left (x \right ) = \frac {2 \sqrt {-6 x}\, x}{3}, y \left (x \right ) = 6 \textit {\_C1}^{3}+\frac {x^{2}}{2 \textit {\_C1}}\right ]\] Mathematica raw input
DSolve[12*x^3 - 2*y[x]*y'[x]^3 + x*y'[x]^4 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(x*diff(y(x),x)^4-2*y(x)*diff(y(x),x)^3+12*x^3 = 0, y(x))
Maple raw output
[y(x) = -2/3*6^(1/2)*x^(3/2), y(x) = 2/3*6^(1/2)*x^(3/2), y(x) = -2/3*(-6*x)^(1/2)*x, y(x) = 2/3*(-6*x)^(1/2)*x, y(x) = 6*_C1^3+1/2/_C1*x^2]