Transforms And Partial Differential Equations: UNIT III: Application Of Partial Differential Equations
Method Of Separation Of Variables
Examples
A powerful method of obtaining particular solutions of a p.d.e. is known as separation of variables or product method.
METHOD OF SEPARATION OF VARIABLES
A powerful method of obtaining
particular solutions of a p.d.e. is known as separation of variables or product
method.
Let z be the dependent variable and
x,y be the independent = X (x) Y (v) variables in a given p.d.e. We assume a
solution that z = where X is a function of x alone and Y is a function of y
alone, substituting this value of z in the p.d.e. is possible to write the
resulting equations so that, one side depends on x alone and the other on y
alone.
In this way, we can get ordinary
differential equations involving X and Y and their derivatives. X and Y can be
found and then ca Z = X(x) Y(y)
Problems on method of separation of variables
Example
3.2.1: Solve by using method of separation of variables the equation 2x
Example
3.2.2: Using the method of separation of variables solve
Transforms And Partial Differential Equations: UNIT III: Application Of Partial Differential Equations : Tag: : Examples - Method Of Separation Of Variables