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Calculus: Differential Equations
 

[ definition ][ example#1][ example#2 ][ points of infexion ]

 

 

 

 

Definition

An equation containing any differential coefficients is called a differential equation.

differential coefficients

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.

differential equations

Example #1

differential eqs. problem#1

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Example #2

differential eq. problem#2

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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.

second derivative for min,max or inflection

A point of inflection has a zero gradient, but the point is not a maximum or a minimum value.

inflection maximum minimum

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:inflexion problem

 

second derivative prob #2

 

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