4.19.49 $-4a^{2}x{y}^{\prime }(x)+a^{2}y(x)+y(x)y^{\prime }(x{)}^2=0$

ODE
$$-4a^{2}x{y}^{\prime }(x)+a^{2}y(x)+y(x)y^{\prime }(x{)}^2=0$$ 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

$$\{[x\left(\mathit{\_}\mathit{T}\right)=({\mathit{\_}\mathit{T}}^2+a^2)\mathit{\_}\mathit{C}\mathit{1}\frac{1}{\sqrt[3]{{\mathit{\_}\mathit{T}}^2-3a^2}}{\mathit{\_}\mathit{T}}^{-\frac{4}{3}},y\left(\mathit{\_}\mathit{T}\right)=4\frac{a^2\mathit{\_}\mathit{C}\mathit{1}}{\sqrt[3]{\mathit{\_}\mathit{T}}\sqrt[3]{{\mathit{\_}\mathit{T}}^2-3a^2}}]\}$$ 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)]