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

The solution for (dy)/(dx)=-x/y ,y(4)=-3 is y=-sqrt(-x^2+25)

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

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

y = - - x^{2} + 25

Solution steps

\frac{d y}{d x} = - \frac{x}{y}

Solve separable ODE:

y = - - x^{2} + 25

y = - - x^{2} + 25

(1 + x) y^{^{'}} = 4 y

x d y + 1 + y^{2} d x = 0

\frac{d y}{d x} + x y = \frac{x}{y ^{2}}, y (1) = 0.5

\frac{1}{x} \frac{d y}{d x} + 4 y = 2

(3 x + 8) (y^{2} + 4) d x - 4 y (x^{2} + 5 x + 6) d y = 0

What is the solution for (dy)/(dx)=-x/y ,y(4)=-3 ?
The solution for (dy)/(dx)=-x/y ,y(4)=-3 is y=-sqrt(-x^2+25)