4.19.46 $y(x)y^{\prime }(x{)}^2=a^{2}x$

ODE
$$y(x)y^{\prime }(x{)}^2=a^{2}x$$ ODE Classification

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

Book solution method
No Missing Variables ODE, Solve for $y^{\prime }$

Mathematica ✓
cpu = 0.0173141 (sec), leaf count = 46

$$\{\{y(x)\to (\frac{3c_1}{2}-a{x}^{3/2}){}^{2/3}\},\{y(x)\to (a{x}^{3/2}+\frac{3c_1}{2}){}^{2/3}\}\}$$

Maple ✓
cpu = 0.026 (sec), leaf count = 40

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

DSolve[y[x]*y'[x]^2 == a^2*x,y[x],x]

Mathematica raw output

{{y[x] -> (-(a*x^(3/2)) + (3*C[1])/2)^(2/3)}, {y[x] -> (a*x^(3/2) + (3*C[1])/2)^
(2/3)}}

Maple raw input

dsolve(y(x)*diff(y(x),x)^2 = a^2*x, y(x),'implicit')

Maple raw output

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