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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

2 y^{^{'}} + 8 y = 1

\frac{1}{x ^{2} + y ^{2}} (x y^{^{'}} - y) = 0

\frac{d x}{d t} = \frac{sin ( t )}{sin ( x )}

\frac{d y}{d x} = 0.1 y (1 - 0.5 y), y (0) = 5000

\frac{d y}{d t} + 0.4 t y = 4 t

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