4.19.49 \(-4 a^2 x y'(x)+a^2 y(x)+y(x) y'(x)^2=0\)

ODE
\[ -4 a^2 x y'(x)+a^2 y(x)+y(x) y'(x)^2=0 \] ODE Classification

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

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

Mathematica
cpu = 600.511 (sec), leaf count = 0 , timed out

$Aborted

Maple
cpu = 0.049 (sec), leaf count = 51

\[ \left \{ [x \left ({\it \_T} \right ) ={ \left ({{\it \_T}}^{2}+{a}^{2} \right ) {\it \_C1}{\frac {1}{\sqrt [3]{{{\it \_T}}^{2}-3\,{a}^{2}}}}{{\it \_T}}^{-{\frac {4}{3}}}},y \left ({\it \_T} \right ) =4\,{\frac {{a}^{2}{\it \_C1}}{\sqrt [3]{{\it \_T}}\sqrt [3]{{{\it \_T}}^{2}-3\,{a}^{2}}}}] \right \} \] Mathematica raw input

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

Mathematica raw output

$Aborted

Maple raw input

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

Maple raw output

[x(_T) = (_T^2+a^2)*_C1/(_T^2-3*a^2)^(1/3)/_T^(4/3), y(_T) = 4*a^2*_C1/_T^(1/3)/
(_T^2-3*a^2)^(1/3)]