4.18.43 $4(2-x)y^{\prime }(x{)}^2+1=0$

ODE
$$4(2-x)y^{\prime }(x{)}^2+1=0$$ ODE Classification

[_quadrature]

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

Mathematica ✓
cpu = 0.00877178 (sec), leaf count = 31

$$\{\{y(x)\to c_1-\sqrt{x-2}\},\{y(x)\to c_1+\sqrt{x-2}\}\}$$

Maple ✓
cpu = 0.024 (sec), leaf count = 23

$$\{y\left(x\right)=-\sqrt{x-2}+\mathit{\_}\mathit{C}\mathit{1},y\left(x\right)=\sqrt{x-2}+\mathit{\_}\mathit{C}\mathit{1}\}$$ Mathematica raw input

DSolve[1 + 4*(2 - x)*y'[x]^2 == 0,y[x],x]

Mathematica raw output

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

Maple raw input

dsolve(4*(2-x)*diff(y(x),x)^2+1 = 0, y(x),'implicit')

Maple raw output

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