What is the solution for (dy)/(dx)=((y+3)(x-1))/((y-2)(x+4)) ?

The solution for (dy)/(dx)=((y+3)(x-1))/((y-2)(x+4)) is y=-5\W(-(x+4}{5e^{\frac{x+c_{1}+3)/5}})-3

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(dy)/(dx)=((y+3)(x-1))/((y-2)(x+4))

\frac{d y}{d x} = \frac{( y + 3 ) ( x - 1 )}{( y - 2 ) ( x + 4 )}

y = - 5 W (- \frac{x + 4}{5 e ^{\frac{x + c _{1} + 3}{5}}}) - 3

Solution steps

\frac{d y}{d x} = \frac{( y + 3 ) ( x - 1 )}{( y - 2 ) ( x + 4 )}

Solve separable ODE:

y = - 5 W (- \frac{x + 4}{5 e ^{\frac{x + c _{1} + 3}{5}}}) - 3

y = - 5 W (- \frac{x + 4}{5 e ^{\frac{x + c _{1} + 3}{5}}}) - 3

\frac{d y}{d x} y = \frac{5}{cos ( x )} + \frac{1}{tan ( x )}

\frac{1}{2} \frac{d y}{d t} + 10 y = 12, y (0) = 0

y^{^{'}} = \frac{6 x y ^{3}}{e ^{3 x}}

y^{^{'}} = 3 y (1 - \frac{y}{4})

\frac{d y}{d t} = 1 - 0.01 y, y (0) = 5

What is the solution for (dy)/(dx)=((y+3)(x-1))/((y-2)(x+4)) ?
The solution for (dy)/(dx)=((y+3)(x-1))/((y-2)(x+4)) is y=-5\W(-(x+4}{5e^{\frac{x+c_{1}+3)/5}})-3