4.18.41 \(4 x y'(x)^2+4 y(x) y'(x)=1\)

ODE
\[ 4 x y'(x)^2+4 y(x) y'(x)=1 \] ODE Classification

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

Book solution method
No Missing Variables ODE, Solve for \(y\)

Mathematica
cpu = 20.4233 (sec), leaf count = 1

\[\text {$\$$Aborted}\]

Maple
cpu = 0.023 (sec), leaf count = 32

\[ \left \{ [x \left ({\it \_T} \right ) ={1 \left ({\frac {1}{12}{{\it \_T}}^{-{\frac {3}{2}}}}+{\it \_C1} \right ) {\frac {1}{\sqrt {{\it \_T}}}}},y \left ({\it \_T} \right ) ={\frac {1}{6\,{{\it \_T}}^{2}} \left (-6\,{{\it \_T}}^{5/2}{\it \_C1}+{\it \_T} \right ) }] \right \} \] Mathematica raw input

DSolve[4*y[x]*y'[x] + 4*x*y'[x]^2 == 1,y[x],x]

Mathematica raw output

$Aborted

Maple raw input

dsolve(4*x*diff(y(x),x)^2+4*y(x)*diff(y(x),x) = 1, y(x),'implicit')

Maple raw output

[x(_T) = 1/_T^(1/2)*(1/12/_T^(3/2)+_C1), y(_T) = 1/6*(-6*_T^(5/2)*_C1+_T)/_T^2]