This section contains worked examples of the type of differential equation which can be solved by integration
Separable Differential EquationsThis section contains worked examples of the type of differential equation which can be solved by direct Integration.
- Separable Differential Equations are differential equations which respect one of the following forms :
- where is a two variable function, also continuous.
- , where and are two real continuous functions.
- A rational function on is a function which can be expressed as where are two polynomials.
Example - Simple Differential Equation
As the equation is of first order, integrate the function twice, i.e.
- A rational function on is a function which can be expressed as a combination of trigonometric functions ().
Example - Simple Cosine
This is the same as
which we integrate in the normal way to yield
Example - Potential example
If a and b are the radii of concentric spherical conductors at potentials of respectively, then V is the potential at a distance r from the centre. Find the value of V if:
and at r=a and at r=b
Substituting in the given values for V and r