Question

How do you solve separable differential equations with initial conditions?

Answer 1

A separable equation typically looks like:

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

by multiplying by `dx` and by `f(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.

For an example of a separable equation with an initial condition, please watch this video: