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

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

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

\frac{d y}{d x} = \frac{x + 1}{2 - y}

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

Solution steps

\frac{d y}{d x} = \frac{x + 1}{2 - y}

Solve separable ODE:

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

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

e^{y} y^{^{'}} = 1

\frac{d x}{x} = \frac{x d y}{y ^{2}}

4 \cdot y^{^{'}} + y = 0

\frac{d y}{d t} = - \frac{y}{15 + t}

\frac{x ^{2}}{y} - 4 x e^{y^{2}} y^{^{'}} = 0

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