What is the solution for (dy)/(dx)=((x-3))/(y+5) ?

The solution for (dy)/(dx)=((x-3))/(y+5) is y=-5+sqrt(x^2-6x+c_{1)+25},y=-sqrt(x^2-6x+c_{1)+25}-5

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(dy)/(dx)=((x-3))/(y+5)

\frac{d y}{d x} = \frac{( x - 3 )}{y + 5}

y = - 5 + x^{2} - 6 x + c_{1} + 25, y = - x^{2} - 6 x + c_{1} + 25 - 5

Solution steps

\frac{d y}{d x} = \frac{( x - 3 )}{y + 5}

Solve separable ODE:

y = - 5 + x^{2} - 6 x + c_{1} + 25, y = - x^{2} - 6 x + c_{1} + 25 - 5

y = - 5 + x^{2} - 6 x + c_{1} + 25, y = - x^{2} - 6 x + c_{1} + 25 - 5

What is the solution for (dy)/(dx)=((x-3))/(y+5) ?
The solution for (dy)/(dx)=((x-3))/(y+5) is y=-5+sqrt(x^2-6x+c_{1)+25},y=-sqrt(x^2-6x+c_{1)+25}-5