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

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

[_quadrature]

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

Mathematica
cpu = 0.0059783 (sec), leaf count = 39

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

Maple
cpu = 0.025 (sec), leaf count = 25

\[ \left \{ y \relax (x ) =-2\,\sqrt {ax}+{\it \_C1},y \relax (x ) =2\,\sqrt {ax}+{\it \_C1} \right \} \] Mathematica raw input

DSolve[x*y'[x]^2 == a,y[x],x]

Mathematica raw output

{{y[x] -> -2*Sqrt[a]*Sqrt[x] + C[1]}, {y[x] -> 2*Sqrt[a]*Sqrt[x] + C[1]}}

Maple raw input

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

Maple raw output

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