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 = 0.165275 (sec), leaf count = 31
\[\left \{\left \{y(x)\to -\sqrt {x-2}+c_1\right \},\left \{y(x)\to \sqrt {x-2}+c_1\right \}\right \}\]
Maple ✓
cpu = 0.075 (sec), leaf count = 23
\[\left [y \left (x \right ) = -\sqrt {x -2}+\textit {\_C1}, y \left (x \right ) = \sqrt {x -2}+\textit {\_C1}\right ]\] 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))
Maple raw output
[y(x) = -(x-2)^(1/2)+_C1, y(x) = (x-2)^(1/2)+_C1]