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

x \to 1 + lim (x - 1)

\int 4 + 6 x + 36 x^{2} d x

(\frac{( 10 - x )}{4})^{2} + \frac{x ^{2}}{4 π}

\int x sin (10 - x) 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