# Differential Equations of First Order and First Degree

1. An equation that involves independent and dependent variables and the derivatives of the dependent variable w.r.t. independent variable is called a differential equation.

dy = sin x dx, etc.
2. A differential equation is said to be ordinary, if the differential coefficients have reference to a single independent variable only and it is said to be partial if there are two or more independent variables. We are concerned with ordinary differential equations only.

For example,

+ 2y = 0

is ordinary differential equation

= 0; = x2 + y

are partial differential equation.

# Order and degree of differential equations

The order of a differential equation is the order of the highest differential coefficient occurring in it.

The degree of a differential equation which is expressed or can be expressed as a polynomial in the derivatives is the degree of the highest order derivative occurring in it, after it has been expressed in a form free from radicals and fractions as far as derivatives are concerned, thus the differential equation:

f(x, y) + Ï† (x, y) + ... = 0 is of order m and degree p.