4.19.46 \(y(x) y'(x)^2=a^2 x\)

ODE
\[ y(x) y'(x)^2=a^2 x \] ODE Classification

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

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

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

\[\left \{\left \{y(x)\to \left (\frac {3 c_1}{2}-a x^{3/2}\right ){}^{2/3}\right \},\left \{y(x)\to \left (a x^{3/2}+\frac {3 c_1}{2}\right ){}^{2/3}\right \}\right \}\]

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

\[ \left \{ [x \left ({\it \_T} \right ) ={{{\it \_T}}^{2}{\it \_C1} \left ({{\it \_T}}^{3}-{a}^{2} \right ) ^{-{\frac {2}{3}}}},y \left ({\it \_T} \right ) ={{a}^{2}{\it \_C1} \left ({{\it \_T}}^{3}-{a}^{2} \right ) ^{-{\frac {2}{3}}}}] \right \} \] 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]