4.18.43 \(4 (2-x) y'(x)^2+1=0\)

ODE
\[ 4 (2-x) y'(x)^2+1=0 \] ODE Classification

[_quadrature]

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

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

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

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

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