Solving Separable Differential Equations

Key Questions

  • How do you solve separable differential equations with initial conditions?

    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:

    Wataru · · Oct 1 2014
  • How do you solve separable differential equations?

    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.

    For more details, please watch this video:

    Wataru · 1 · Sep 19 2014

Questions

Applications of Definite Integrals