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1

Solved example of Separable differential equations

$\frac{dy}{dx}=-\frac{x}{y}$

2

Multiply both sides of the equation by $dx$

$dy=-\left(\frac{x}{y}\right)dx$

3

Integrate both sides, the left side with respect to $y$, and the right side with respect to $x$

$\int1dy=\int-1dx$

4

The integral of a constant is equal to the constant times the integral's variable

$y=\int-1dx$

5

The integral of a constant is equal to the constant times the integral's variable

$y=-x$

6

As the integral that we are solving is an indefinite integral, when we finish we must add the constant of integration

$y=-x+C_0$