Basic Concepts of Differential Equation




We are already familiar with the equations of the type: 
`x_2` – 3x + 3 = 0 ... (1) 
sin x + cos x = 0   ... (2) 
x + y = 7               ... (3)
Let us consider the equation:
x`(dy)/(dx)` + y = 0     ... (4)

We see that equations (1), (2) and (3) involve independent and/or dependent variable (variables) only but equation (4) involves variables as well as derivative of the dependent variable y with respect to the independent variable x. Such an equation is called a differential equation.
In general, an equation involving  derivative (derivatives) of the dependent variable with respect to independent variable (variables) is called a differential equation.
A differential equation involving derivatives of the dependent variable with respect to only one independent variable is called an ordinary differential equation, e.g.,differential equation. 

2`(d^2y)/(dx^2) + ((dy)/(dx))^3` = 0  is an ordinary differential equation 
.... (5)

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Differential Equations [00:03:47]

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