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# Order and degree of a differential equation

The highest order derivative present in the differential equation is the order of the differential equation.

Order and degree of a differential equation

The highest order derivative present in the differential equation is the order of the differential equation.

Degree is the highest power of the highest order derivative in the differential equation, after the equation has been cleared from fractions and the radicals as for as the derivatives are concerned.

For example, consider the differential equation Here the highest order derivatives is ( i.e 3rd order derivative). So the order of the differential equation is 3.

Now the power of highest order derivative is 1.

The degree of the differential equation is 1.

Example 4.1

Find the order and degree of the following differential equations. Solution  ## Family of Curves

Sometimes a family of curves can be represented by a single equation with one or more arbitrary constants. By assigning different values for constants, we get a family of curves. The arbitrary constants are called the parameters of the family.

For example,

(i)   y 2 = 4ax represents the equation of a family of parabolas having the origin as vertex where ‘a’ is the parameter.

(ii) x 2 + y2 = a2 represents the equation of family of circles having the origin as centre, where ‘a’ is the parameter.

(iii) y = mx + c represents the equation of a family of straight lines in a plane, where m and c are parameters.

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12th Business Maths and Statistics : Chapter 4 : Differential Equations : Order and degree of a differential equation | Example Solved Problems with Answer, Solution, Formula