What is the solution for (dy)/(dx)=(x(y-4)+y-4)/(x(y-6)-3(y-6)) ?

The solution for (dy)/(dx)=(x(y-4)+y-4)/(x(y-6)-3(y-6)) is y=-2\W(-1/(2e^{(x+c_{1)-4)/2}(x-3)^2})+4

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(dy)/(dx)=(x(y-4)+y-4)/(x(y-6)-3(y-6))

\frac{d y}{d x} = \frac{x ( y - 4 ) + y - 4}{x ( y - 6 ) - 3 ( y - 6 )}

y = - 2 W (- \frac{1}{2 e ^{\frac{x + c _{1} - 4}{2}} ( x - 3 ) ^{2}}) + 4

Solution steps

\frac{d y}{d x} = \frac{x ( y - 4 ) + y - 4}{x ( y - 6 ) - 3 ( y - 6 )}

Solve separable ODE:

y = - 2 W (- \frac{1}{2 e ^{\frac{x + c _{1} - 4}{2}} ( x - 3 ) ^{2}}) + 4

y = - 2 W (- \frac{1}{2 e ^{\frac{x + c _{1} - 4}{2}} ( x - 3 ) ^{2}}) + 4

\frac{d y}{d x} = y^{2} + 4 y + 5

\frac{d y}{y ^{2}} = \frac{d x}{- x ^{2} + 4}

x e^{x} d x - 3 y^{2} d y = 0

y^{^{'}} = y (5 - y) - \frac{25}{4}

y^{^{'}} = \frac{x ^{2} y ^{2}}{1 + x ^{2}}

What is the solution for (dy)/(dx)=(x(y-4)+y-4)/(x(y-6)-3(y-6)) ?
The solution for (dy)/(dx)=(x(y-4)+y-4)/(x(y-6)-3(y-6)) is y=-2\W(-1/(2e^{(x+c_{1)-4)/2}(x-3)^2})+4