4.18.17 \(x y'(x)^2-(3 x-y(x)) y'(x)+y(x)=0\)

ODE
\[ x y'(x)^2-(3 x-y(x)) y'(x)+y(x)=0 \] ODE Classification

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

Book solution method
Clairaut’s equation and related types, d’Alembert’s equation (also call Lagrange’s)

Mathematica
cpu = 604.473 (sec), leaf count = 0 , timed out

$Aborted

Maple
cpu = 0.043 (sec), leaf count = 29

\[ \left \{ y \relax (x ) =x,[x \left ({\it \_T} \right ) ={ \left (1+{\it \_T} \right ) {\it \_C1}{{\it \_T}}^{-{\frac {3}{2}}}},y \left ({\it \_T} \right ) =-{ \left ({\it \_T}-3 \right ) {\it \_C1}{\frac {1}{\sqrt {{\it \_T}}}}}] \right \} \] Mathematica raw input

DSolve[y[x] - (3*x - y[x])*y'[x] + x*y'[x]^2 == 0,y[x],x]

Mathematica raw output

$Aborted

Maple raw input

dsolve(x*diff(y(x),x)^2-(3*x-y(x))*diff(y(x),x)+y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = x, [x(_T) = (1+_T)*_C1/_T^(3/2), y(_T) = -1/_T^(1/2)*(_T-3)*_C1]