Question

How do you solve separable first-order differential equations?

Answer 1

A separable equation typically looks like:
`{dy}/{dx}={g(x)}/{f(y)}`.

By multiplying by `dx` and by `g(y)` to separate `x`'s and `y`'s,
`Rightarrow f(y)dy=g(x)dx`

By integrating both sides,
`Rightarrow int f(y)dy=int g(x)dx`,
which gives us the solution expressed implicitly:

`Rightarrow F(y)=G(x)+C`,
where `F` and `G` are antiderivatives of `f` and `g`, respectively.

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