## FANDOM

17 Pages

A first order differential equation is called seperable if it can be written as

${{dy \over dx} = f(x)g(y)}$.

In this case, the equation can informally be written as

${g(y) dy = f(x) dx}$.

By taking the integral of both sides, the solution can be written as

${F(y(x)) = G(x) + C}$

where,

${F(y) = \int f(y) dy, G(x) = \int g(x) dx}$

and  is a constant of integration.

## Example

${{dy \over dx} = y sin(x)}$

${\Rightarrow {1 \over y} dy = sin(x) dx}$

${\Rightarrow \int {1\over y} dy = \int sin(x) dx}$

${\Rightarrow ln|y| = -cos(x) + C}$

${\Rightarrow y = e^{-cos(x) + C}}$

${\Rightarrow y = De^{-cos(x)}}$