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Session

Differential Equations - 3

Session Objectives

- Linear Differential Equations

- Applications of Differential Equations

- Differential Equations of Second Order

- Class Exercise

Linear Differential Equations

Linear Differential Equations type-1

where P and Q are the functions of x, or

constants.

Example 1

Solution Cont.

Example -2

Solution The given differential equation is

Solution Cont.

The solution is given by

Example 3

Solution Cont.

The solution is given by

Linear Differential Equations type 2

where P and Q are the functions of y, or

constants.

Example - 4

Solution The given differential equation is

Solution Cont.

The solution is given by

Applications of Differential Equations

Differential equations are used to solve problems

of science and engineering.

Example - 5

A population grows at the rate of 5 per year.

How long does it take for the population to

double? Use differential equation for it.

Solution Let the initial population be P0 and

let the population after t years

be P, then

Integrating both sides

Solution Cont.

At t 0, P P0

Example - 6

Solution Cont.

The curve passes through the point (3, 4).

Differential Equations of Second Order

is the required general solution of the given

differential equation.

Example -7

Solution The given differential equation is

Solution Cont.

Example 8

Integrating (i), we get

Solution Cont.

Again integrating both sides of (ii), we get

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