Order and Degree of a Differential Equation:

The order of differential equation is order of highest order derivative appearing in equation.

For instance:

The orders of differential equations (1), (2), (3), (4), (5) and (6) are 1, 2, 1, 3, 2 and 2 respectively.

The degree of differential equation is degree of the highest order derivative involved in it, when differential coefficients are free from radicals and fractions (that is write differential equations as polynomial in the derivatives)

For Example:

The degrees of differential equations (1), (2), (3), (4), (5) and (6) are 1, 1, 1, 4, 3 and 2 respectively.

Illustration: Find out the order and degree (if defined) of the following differential equations:

              (i)               (ii) 

Solution : (i) The given differential equation is re-written as

                . Thus its order is 3 and degree 2.

                (ii) . Thus its order is 2 and degree 1.

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