4.18.38 $4x{y}^{\prime }(x{)}^2=(a-3x{)}^2$

ODE
$$4x{y}^{\prime }(x{)}^2=(a-3x{)}^2$$ ODE Classification

[_quadrature]

Book solution method
Missing Variables ODE, Dependent variable missing, Solve for $y^{\prime }$

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

$$\{\{y(x)\to \sqrt{x}(a-x)+c_1\},\{y(x)\to \sqrt{x}(x-a)+c_1\}\}$$

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

$$\{y\left(x\right)=-\sqrt{x}(a-x)+\mathit{\_}\mathit{C}\mathit{1},y\left(x\right)=\sqrt{x}(a-x)+\mathit{\_}\mathit{C}\mathit{1}\}$$ 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