# Differential Equations of First Order and First Degree

- 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. - 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.
*y*= 0*x*^{2}+*y*

# 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*.