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