4.18.38 \(4 x y'(x)^2=(a-3 x)^2\)

ODE
\[ 4 x y'(x)^2=(a-3 x)^2 \] ODE Classification

[_quadrature]

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

Mathematica
cpu = 0.013433 (sec), leaf count = 37

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

Maple
cpu = 0.034 (sec), leaf count = 30

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

DSolve[4*x*y'[x]^2 == (a - 3*x)^2,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(4*x*diff(y(x),x)^2 = (a-3*x)^2, y(x),'implicit')

Maple raw output

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