Solving Separable Differential Equations
Key Questions

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:

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:
Questions
Applications of Definite Integrals

Solving Separable Differential Equations

Slope Fields

Exponential Growth and Decay Models

Logistic Growth Models

Net Change: Motion on a Line

Determining the Surface Area of a Solid of Revolution

Determining the Length of a Curve

Determining the Volume of a Solid of Revolution

Determining Work and Fluid Force

The Average Value of a Function