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

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

[_quadrature]

Book solution method
Missing Variables ODE, Independent variable missing, Solve for \(y'\)

Mathematica
cpu = 0.0142983 (sec), leaf count = 54

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

Maple
cpu = 0.031 (sec), leaf count = 39

\[ \left \{ x-{\frac {2\, \left (y \relax (x ) \right ) ^{2}}{3}{\frac {1}{\sqrt {ay \relax (x ) }}}}-{\it \_C1}=0,x+{\frac {2\, \left (y \relax (x ) \right ) ^{2}}{3}{\frac {1}{\sqrt {ay \relax (x ) }}}}-{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[y[x]*y'[x]^2 == a,y[x],x]

Mathematica raw output

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

Maple raw input

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

Maple raw output

x-2/3*y(x)^2/(a*y(x))^(1/2)-_C1 = 0, x+2/3*y(x)^2/(a*y(x))^(1/2)-_C1 = 0