Method of Separation of Variables

Method of Separation of Variables
In this lecture we discuss the method of separation of variables. It involves a solution which breaks up into a product of two functions each of which contains only one of the variables. The following examples explain this method.
Example 1: Apply the method of separation of variables to solve

Solution :
where is a function of alone and that of given

Substituting in the given equation, we have















Example 2: Solve by using the method of separation of variables,

Solution :









Example 3: Solve
Solution :






Example 4: Solve
Solution :










H.W: Apply the method of separation of variables to solve the PDE



Method of Separation of Variables
In this lecture we discuss the method of separation of variables. It involves a solution which breaks up into a product of two functions each of which contains only one of the variables. The following examples explain this method.
Example 1: Apply the method of separation of variables to solve

Solution :
where is a function of alone and that of given

Substituting in the given equation, we have















Example 2: Solve by using the method of separation of variables,

Solution :









Example 3: Solve
Solution :






Example 4: Solve
Solution :










H.W: Apply the method of separation of variables to solve the PDE