4.862   ay(x)+ xy′(x)2 − y(x)y′(x) = 0

ODE

ay(x)+ xy′(x)2 − y(x)y′(x ) = 0

ODE Classification

[[_homogeneous, `class A`], _rational, _dAlembert]

Book solution method
No Missing Variables ODE, Solve for x

Mathematica
cpu = 0.805737 (sec), leaf count = 158

(     ⌊       ∘ ---∘ --------                                              ⌋      ⌊ ∘ ---∘ --------                                                    ⌋ )
{               y(x)  y(x)− 4a                    ( ∘ --------- ∘ ----)                y(x)  y(x)− 4a                  (∘ ---------  ∘ ----)               }
 Solve⌈ y(x)-+ ---x----x------+ 4c1 + 2 log(x) = 4log  y(x)− 4a+   y(x)  ,y(x)⌉ ,Solve⌈ ---x----x------+ 4c1 = y(x-)+ 4log    y(x)-− 4a+   y(x)  + 2log(x),y(x)⌉
(       ax           a                                x            x                       a               ax             x           x                  )

Maple
cpu = 0.027 (sec), leaf count = 40

{                           ( -T)− 1          2   ( -T)− 1}
 y(x) = 0,[x(-T) = (-T − a) C1 e a  ,y ( T) = T  C1 e a   ]

Mathematica raw input

DSolve[a*y[x] - y[x]*y'[x] + x*y'[x]^2 == 0,y[x],x]

Mathematica raw output

{Solve[4*C[1] + 2*Log[x] + y[x]/(a*x) + (Sqrt[y[x]/x]*Sqrt[-4*a + y[x]/x])/a == 
4*Log[Sqrt[y[x]/x] + Sqrt[-4*a + y[x]/x]], y[x]], Solve[4*C[1] + (Sqrt[y[x]/x]*S
qrt[-4*a + y[x]/x])/a == 2*Log[x] + 4*Log[Sqrt[y[x]/x] + Sqrt[-4*a + y[x]/x]] + 
y[x]/(a*x), y[x]]}

Maple raw input

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

Maple raw output

y(x) = 0, [x(_T) = (_T-a)*_C1/exp(_T/a), y(_T) = _T^2*_C1/exp(_T/a)]