# Basic Concepts of Differential Equation

## Notes

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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