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

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

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: ( x^{2} + x +1) dx + ( y^{2} - y + 3)dy = 0

*Solution:*

**Example 4.12**

The marginal cost function of manufacturing *x* gloves is 6 + 10*x* − 6*x*^{2} .
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? (log* _{e}*
2 = 0.6931)

*Solution:*

Tags : Example Solved Problems with Answer, Solution, Formula | Differential Equations , 12th Business Maths and Statistics : Chapter 4 : Differential Equations

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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

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