ODE
\[ 4 x^2+x y'(x)^3-2 y(x) y'(x)^2=0 \] ODE Classification
[[_1st_order, _with_linear_symmetries]]
Book solution method
No Missing Variables ODE, Solve for \(y\)
Mathematica ✗
cpu = 600.014 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.656 (sec), leaf count = 97
\[ \left \{ \left ( y \left ( x \right ) \right ) ^{3}-{\frac {27\,{x}^{4}}{8}}=0,[x \left ( {\it \_T} \right ) ={\frac {{\it \_T}\, \left ( \left ( {{\it \_T}}^{2}-{\it \_C1} \right ) {\it csgn} \left ( -{{\it \_T}}^{2}+{\it \_C1} \right ) -{{\it \_T}}^{2} \right ) }{8}},y \left ( {\it \_T} \right ) =-{\frac {{\it \_C1}\,{{\it \_T}}^{2}}{16}}+{\frac {{{\it \_C1}}^{2}}{32}}],[x \left ( {\it \_T} \right ) ={\frac {{\it \_T}\, \left ( \left ( {{\it \_T}}^{2}+{\it \_C1} \right ) {\it csgn} \left ( {{\it \_T}}^{2}+{\it \_C1} \right ) -{{\it \_T}}^{2} \right ) }{8}},y \left ( {\it \_T} \right ) ={\frac {{\it \_C1}\,{{\it \_T}}^{2}}{16}}+{\frac {{{\it \_C1}}^{2}}{32}}] \right \} \] Mathematica raw input
DSolve[4*x^2 - 2*y[x]*y'[x]^2 + x*y'[x]^3 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve(x*diff(y(x),x)^3-2*y(x)*diff(y(x),x)^2+4*x^2 = 0, y(x),'implicit')
Maple raw output
y(x)^3-27/8*x^4 = 0, [x(_T) = 1/8*_T*((_T^2-_C1)*csgn(-_T^2+_C1)-_T^2), y(_T) = -1/16*_C1*_T^2+1/32*_C1^2], [x(_T) = 1/8*_T*((_T^2+_C1)*csgn(_T^2+_C1)-_T^2), y(_T) = 1/16*_C1*_T^2+1/32*_C1^2]