How do you solve separable differential equations with initial conditions?

1 Answer
Oct 1, 2014

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: