What is the solution for (dy)/(dx)=((2-x))/((y-1)) ?

The solution for (dy)/(dx)=((2-x))/((y-1)) is y=1+sqrt(-x^2+4x+c_{1)+1},y=1-sqrt(-x^2+4x+c_{1)+1}

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(dy)/(dx)=((2-x))/((y-1))

\frac{d y}{d x} = \frac{( 2 - x )}{( y - 1 )}

y = 1 + - x^{2} + 4 x + c_{1} + 1, y = 1 - - x^{2} + 4 x + c_{1} + 1

Solution steps

\frac{d y}{d x} = \frac{( 2 - x )}{( y - 1 )}

Solve separable ODE:

y = 1 + - x^{2} + 4 x + c_{1} + 1, y = 1 - - x^{2} + 4 x + c_{1} + 1

y = 1 + - x^{2} + 4 x + c_{1} + 1, y = 1 - - x^{2} + 4 x + c_{1} + 1

\frac{d v}{d t} = g - \frac{1}{40} v

e^{x + 2 y} - e^{- 3 y} y^{^{'}} = 0

4 y^{^{'}} = 1 + x + y + x y

y^{^{'}} + 18 y^{^{'}} + 81 y = 0

\frac{d y}{d x} = (- n y)

What is the solution for (dy)/(dx)=((2-x))/((y-1)) ?
The solution for (dy)/(dx)=((2-x))/((y-1)) is y=1+sqrt(-x^2+4x+c_{1)+1},y=1-sqrt(-x^2+4x+c_{1)+1}