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

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

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

y (1 - x) - x \frac{d y}{d x} = 0

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

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 )}

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