4.810   4x5y′(x)− 12x4y(x) + y′(x)2 = 0

ODE

4x5y′(x)− 12x4y(x)+ y′(x)2 = 0

ODE Classification

[[_1st_order, _with_linear_symmetries]]

Book solution method
No Missing Variables ODE, Solve for y

Mathematica
cpu = 1.09311 (sec), leaf count = 217

(     ⌊    ---------            -------------(   (        )     (       )       (  ---------    ))         ⌋      ⌊     ---------           -------------(     (        )     (       )       (  ---------    ))         ⌋)
{       x2∘x6 + 3y(x )log(y(x)) +∘ x4 (x6 + 3y(x)) log -x6- + 1 − log 3y(x6) +1  + 2log ∘ x6 + 3y(x)+ x3                   x2∘ x6 + 3y(x)log(y(x)) + ∘x4 (x6 + 3y(x)) − log x
 Solve⌈ -----------------------------------------∘3y(x)-----------x--------------------------------= c1,y(x)⌉ ,Solve⌈ ------------------------------------------∘-3y(x)------------x--------------------------------= c1,y(x)⌉
(                                             6x2  x6 + 3y(x)                                                                                              6x2  x6 + 3y(x)                                                )

Maple
cpu = 0.205 (sec), leaf count = 23

{        x6            3   3 C12 }
 y (x) = −-3 ,y (x) =-C1x +  --4--

Mathematica raw input

DSolve[-12*x^4*y[x] + 4*x^5*y'[x] + y'[x]^2 == 0,y[x],x]

Mathematica raw output

{Solve[(x^2*Log[y[x]]*Sqrt[x^6 + 3*y[x]] + (Log[1 + x^6/(3*y[x])] - Log[1 + (3*y
[x])/x^6] + 2*Log[x^3 + Sqrt[x^6 + 3*y[x]]])*Sqrt[x^4*(x^6 + 3*y[x])])/(6*x^2*Sq
rt[x^6 + 3*y[x]]) == C[1], y[x]], Solve[(x^2*Log[y[x]]*Sqrt[x^6 + 3*y[x]] + (-Lo
g[1 + x^6/(3*y[x])] + Log[1 + (3*y[x])/x^6] - 2*Log[x^3 + Sqrt[x^6 + 3*y[x]]])*S
qrt[x^4*(x^6 + 3*y[x])])/(6*x^2*Sqrt[x^6 + 3*y[x]]) == C[1], y[x]]}

Maple raw input

dsolve(diff(y(x),x)^2+4*x^5*diff(y(x),x)-12*x^4*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = -1/3*x^6, y(x) = _C1*x^3+3/4*_C1^2