Definition
An equation containing any differential coefficients is called a differential equation.
The solution of a differential equation is an equation relating x and y and containing no differential coefficients.
General & particular Solution
The General Solution includes some unknown constant in the solution of a differential equation.
When some data is given, say the coordinates of a point, then a Particular Solution can be formed.
Example #1
Example #2
Points of Inflection(Inflexion)
The value of the second derivative can give an indication whether at a point a function has a maximum, minimum or an inflection.These are all called stationary points.
A point of inflection has a zero gradient, but the point is not a maximum or a minimum value.
It is where the gradient of a curve decreases(or increases)to zero before increasing(or decreasing)again, but not changing from a negative to a positive value or vice versa.
Example
Find the stationary points of the function:
