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

The solution for (dy)/(dx)=((x-4))/(y+3) is y=-3+sqrt(x^2-8x+c_{1)+9},y=-sqrt(x^2-8x+c_{1)+9}-3

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

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

y = - 3 + x^{2} - 8 x + c_{1} + 9, y = - x^{2} - 8 x + c_{1} + 9 - 3

Solution steps

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

Solve separable ODE:

y = - 3 + x^{2} - 8 x + c_{1} + 9, y = - x^{2} - 8 x + c_{1} + 9 - 3

y = - 3 + x^{2} - 8 x + c_{1} + 9, y = - x^{2} - 8 x + c_{1} + 9 - 3

(1, - 7), (2, - 1)

\int e^{\frac{x}{3}} d x

ln (x + 1 + x^{2} + 2 x), 1

\int_{- 6}^{- 1} 8 d x

\int (x + 4)^{2} (x - 4) d x

What is the solution for (dy)/(dx)=((x-4))/(y+3) ?
The solution for (dy)/(dx)=((x-4))/(y+3) is y=-3+sqrt(x^2-8x+c_{1)+9},y=-sqrt(x^2-8x+c_{1)+9}-3