Turn on thread page Beta

Question about second order differential equations watch

    • Thread Starter
    Offline

    2
    ReputationRep:
    Say we have a second order ODE

    ay'' + by' + cy = f(x) + g(x)

    where f(x) and g(x) are functions of x.

    And say we want to find a particular integral for this.

    What if we find a particular integral to
    ay'' + by' + cy = f(x)
    and one to
    ay'' + by' + cy = g(x)
    ?

    If we add together these particular integrals will we get a particular integral for
    ay'' + by' + cy = f(x) + g(x)
    ?
    Offline

    2
    ReputationRep:
    (Original post by gangsta316)
    Say we have a second order ODE

    ay'' + by' + cy = f(x) + g(x)

    where f(x) and g(x) are functions of x.

    And say we want to find a particular integral for this.

    What if we find a particular integral to
    ay'' + by' + cy = f(x)
    and one to
    ay'' + by' + cy = g(x)
    ?

    If we add together these particular integrals will we get a particular integral for
    ay'' + by' + cy = f(x) + g(x)
    ?
    Write the differential operator as L. L is linear from the chain rule.

    then if L(y)=f(x) and L(w)=g(x)

    then L(y+w) = L(y) + L(w) = f(x) + g(x)
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: February 10, 2010
The home of Results and Clearing

2,504

people online now

1,567,000

students helped last year

University open days

  1. Keele University
    General Open Day Undergraduate
    Sun, 19 Aug '18
  2. University of Melbourne
    Open Day Undergraduate
    Sun, 19 Aug '18
  3. Sheffield Hallam University
    City Campus Undergraduate
    Tue, 21 Aug '18
Poll
A-level students - how do you feel about your results?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.