Page 118 - DMTH202_BASIC_MATHEMATICS_II

Unit 9: Solution of Differential Equation

distance of a moving particle, variation of current in an electric circuit, in mechanical systems, Notes
agriculture, etc. A differential equation involves independent variables, dependent variables,
their derivatives and constants. These equations are solved and the solutions thus obtained are
interpreted in the context of the problem.

9.1 Order & Degree of Differential Equation

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

The degree of a differential equation is the degree of the highest derivative occurring in it, after
the equation has been expressed in a form free from radials and fractions so far as the derivatives
are concerned.
Thus from the above differential equations:
(i) is of the first order and first degree;
(ii) is of the second order and first degree;

(iii) is of the first order and second degree;
(iv) is of the second order and second degree;

Did u know? Equation of degree higher than one is also called non-linear.

Self Assessment

Fill in the blanks:
1. A ................................... involves independent variables, dependent variables, their
derivatives and constants.
2. The ................................... of a differential equation is the order of highest derivative appearing
in the equation.
3. The ................................... of a differential equation is the degree of the highest derivative
occurring in it, after the equation has been expressed in a form free from radials and
fractions so far as the derivatives are concerned.
4. Equation of degree higher than one is also called ................................... .

9.2 Solution of a Differential Equation

Any relation between the dependent and independent variables, when substituted in the differential
equation, reduces it to an identity is called a solution or integral of the differential equation.
For example, the equation y = A cosx + B sinx is the solution of the differential equation
2
d y
 y  0 . Because, we have, y = A cosx + B sinx.
dx 2
dy
Upon differentiating it,  A sinx + B cosx.
dx
Again differentiation gives,
2
d y
 (A cosx + B sinx).
dx 2

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