What is the solution for (dy)/(dx)=-x/y ,y(0)=4 ?

The solution for (dy)/(dx)=-x/y ,y(0)=4 is y=sqrt(-x^2+16)

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(dy)/(dx)=-x/y ,y(0)=4

\frac{d y}{d x} = - \frac{x}{y}, y (0) = 4

y = - x^{2} + 16

Solution steps

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

Solve separable ODE:

y = - x^{2} + 16

y = - x^{2} + 16

y^{^{'}} = 2 y, y (0) = 5

\frac{d y}{d x} = \frac{y ( 5 x - 2 )}{x ( 1 - 3 y )}

\frac{d y}{d x} = e^{3 x - 4 y}

y^{^{'}} = \frac{t}{t ^{2} y + y}, y (0) = 7

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

What is the solution for (dy)/(dx)=-x/y ,y(0)=4 ?
The solution for (dy)/(dx)=-x/y ,y(0)=4 is y=sqrt(-x^2+16)