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Then we can separate the two variables, collect the x's on one side and the y's on the other side, then integrate to get the (n-1) derivative, and integrating again to get the (n-2) derivative, until we have found the function y. For example, for the derivative n = 1:

Then we can separate the two variables, collect the x's on one side and the y's on the other side, then integrate to get the (n-1) derivative, and integrating again to get the (n-2) derivative, until we have found the function y. For example, for the derivative n = 1:

<math> \frac{dy}{dx} = F(x)G(y)

<math> \frac{dy}{dx} = F(x)G(y)</math>

\frac{dy}{G(y)} = F(x)dx

<math>\frac{dy}{G(y)} = F(x)dx </math>

\int\frac{dy}{G(y)} = \int F(x)dx </math>

<math>\int\frac{dy}{G(y)} = \int F(x)dx </math>

The solution is then given implicitly by the expression:

The solution is then given implicitly by the expression: