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# First order and first degree differential

A differential equation of first order and first degree can be written as f( x, y, dy/dx) = 0.

First order and first degree differential

A differential equation of first order and first degree can be written as f( x, y, dy/dx) = 0.

Here we will discuss the solution of few types of

## General solution and particular solution

For any differential equations it is possible to find the general solution and particular solution.

## Differential Equation in which variables are separable

If in an equation it is possible to collect all the terms of x and dx on one side and all the terms of y and dy on the other side, then the variables are said to be separable. Thus the general form of such an equation is

f(x)dx = g(y)dy (or) f(x)dx + g(y)dy = 0

By direct integration we get the solution.

Example 4.6

Solve: ( x2 + x +1) dx + ( y2 - y + 3)dy  = 0

Solution:

Example 4.12

The marginal cost function of manufacturing x gloves is 6 + 10x 6x2 . The total cost of producing a pair of gloves is 100. Find the total and average cost function.

Solution:

Example 4.13

The normal lines to a given curve at each point ( x, y) on the curve pass through the point (1,0). The curve passes through the point (1,2). Formulate the differential equation representing the problem and hence find the equation of the curve.

Solution:

Example 4.14

The sum of 2,000 is compounded continuously, the nominal rate of interest being 5% per annum. In how many years will the amount be double the original principal? (loge 2 = 0.6931)

Solution:

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12th Business Maths and Statistics : Chapter 4 : Differential Equations : First order and first degree differential | Example Solved Problems with Answer, Solution, Formula | Differential Equations