This is not the document you are looking for? Use the search form below to find more!

Report

# Differential Equations

Document Description
Differential equation is a type of equation which contains derivatives in it. The derivative may de partial deerivative or a ordinary derivative.The eqution may contain derivative of any order.It the equation contain [dy/dx] then it is a differential equation of first order or first order differential equation,if the equation contain (d^2y)/(dx^2)] then it is second order differential equation and so on for higher order differential equations. Differential equations has wide range of application ,one of the famous application is in newtons 2nd law,it gives us the equation F=ma ,where a is the acceleration.Here a is rate of change of velocity with respect to time or second derivative of position.If v is the velocity then a= [(dv)/dt] or in terms of position a= [(d^2u)/(dt^2)] , where u is the position. In differential equations there are different methods to find the solution for the given differential equation. One of the methods to solve the differential equation is known as variable separable method. Now let us see few examples to solve differential equation using variable separable method.
File Details
• Added: November, 11th 2011
• Reads: 225
• Downloads: 0
• File size: 45.64kb
• Pages: 6
• Tags: differential equations, solving equations, graphing linear equations
• content preview
Submitter
Embed Code:

#### Add New Comment

Related Documents

## Differential Equations

by: mahesh4528, 3 pages

Differential equation is a type of equation which contains derivatives in it. The derivative may de partial deerivative or a ordinary derivative.The eqution may contain derivative of any order.It the ...

## Differential Equations

by: kamlesh, 4 pages

Differential equation is a type of equation which contains derivatives in it. The derivative may de partial deerivative or a ordinary derivative.The eqution may contain derivative of any order.It the ...

## Differential Equations

by: ramsingh11, 6 pages

Differential Equation is a type of equation which contains derivatives in it. The derivative may de partial deerivative or a ordinary derivative.The eqution may contain derivative of any order. It ...

## Higher Order Linear Differential equations

by: nishagoyal, 4 pages

Differentiation is important and interesting part of mathematics. We use differentiation process for calculating the rate of particular function with respect to particular variable like f(x) is a ...

## Qualitative Solutions To Differential Equations

by: nishagoyal, 4 pages

n differential equation we study the equations which are changed when their parameters changed or it is the study of anything that changes. From the study of differential, we learn that the ...

## Differential Equations and Mathematical Modelling

by: nishagoyal, 3 pages

Differential Equations and Mathematical Modelling A mathematical model for any system is the description of that system which uses the mathematical concepts related to the differential equation and ...

## Differential Equations

by: tutorvistateam_team, 4 pages

Today I am going to tell you about a very interesting field of mathematics: differential equations. A differential equation is an equation for the functions which are unknown and are consisting of ...

## National Work Shop On Application of Fractional Calculus in Engineering Physical Law and Solving Extra Ordinary Differential Equations of Fractional Order

by: sougata chatterjee, 54 pages

A modern approach to Solve Extra Ordinary Differential Equations Series reaction of several internal-modes generated to external perturbation. No Laplace Transformation. No discretization required. ...

## Solving Differential Equations

by: vistateam123, 4 pages

Mathematics is a kind of subject in which problems are to be represented or converted in such a form which can be easily understood by students so that they can further solve it, because before ...

## Differential Equations Solver

by: vistateam123, 4 pages

Mathematics is a kind of subject in which problems are to be represented or converted in such a form which can be easily understood by students so that they can further solve it, because before ...

Content Preview
Differential Equations
Differential equation is a type of equation which contains derivatives in it. The derivative may de
partial deerivative or a ordinary derivative.The eqution may contain derivative of any order.It the
equation contain [dy/dx] then it is a differential equation of first order or first order differential
equation,if the equation contain (d^2y)/(dx^2)] then it is second order differential equation and
so on for higher order differential equations.
Differential equations has wide range of application ,one of the famous application is in newtons
2nd law,it gives us the equation F=ma ,where a is the acceleration.Here a is rate of change of
velocity with respect to time or second derivative of position.If v is the velocity then a= [(dv)/dt]
or in terms of position a= [(d^2u)/(dt^2)] , where u is the position.
In differential equations there are different methods to find the solution for the given differential
equation. One of the methods to solve the differential equation is known as variable separable
method. Now let us see few examples to solve differential equation using variable separable
method.

Learn More about Solving Equations

Solving Differential Equations
Back to Top
Below are the examples on solving differential equations using variable separable method.
Example 1 :-
Solve the following differential equation using variable separable method.
[ dy/dx] = 3x + 7.
Solution :-
Given: [dy/dx] = 3x + 7
dy = (5x + 7) dx
Here, the variables are separated, so let's integrate.
[int] dy = [int] (3x + 7 ) dx
y = 3 [((x^2)/(2))] + 7x + c.
Here, c is the constant of integration.

Read More on Graphing Linear Equations

Example 2 :-
Solve the following differential equation using variable separable method.
[ dy/dx] = sinx - 3x.
Solution :-
Given: [ dy/dx] = sinx - 3x
dy = (sinx -3 x) dx
Here, the variables are separated, so let's integrate.
[int] dy = [int] ( sinx - 3x) dx
y = -cosx - 3 [((x^2)/(2))] + c.
Hence, the solution of the differential equation.
Example 3 :-
Solve the following differential equation using variable separable method.
(x +1) [dy/dx ] = x2.

Solution :-
Given: (x +1) [dy/dx] = x2
[ dy/dx] = [((x^2)/ (x +1))]
[ dy/dx] = x - 1 + [1/(x +1)]
dy = [x - 1 + [1/(x +1)] ] dx
Here, the variables are separated, so let's integrate.
[int] dy = [int] [ x - 1 + [1/(x+1)] ]dx, y = [ (x^2)/(2)] -x + ln(x +1) + c.
Example 4 :-
Solve the following differential equation using variable separable method.
[dy/dx] + y = 1.
Solution :-
Given: [dy/dx] + y = 1
[ dy/dx] = 1 - y
[(dy)/(1-y) ] = dx

Here, the variables are separated, so let's integrate.

[int] [(dy)/(1-y) ] = [int dx]
ln(1-y) = x + c
1 - y = e(x +c)
= ex ec
1 - y = k ex
Therefore, the solution is y = 1 - k ex.

Thank You
TutorVista.com

# Document Outline

• ﾿
• ﾿

Download
Differential Equations

Your download will begin in a moment.
If it doesn't, click here to try again.

Share Differential Equations to:

Insert your wordpress URL:

example:

http://myblog.wordpress.com/
or
http://myblog.com/

Share Differential Equations as:

From:

To:

Share Differential Equations.

Enter two words as shown below. If you cannot read the words, click the refresh icon.

Share Differential Equations as:

Copy html code above and paste to your web page.