Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta

2nd order homogeneous differentials equations watch

    • Thread Starter

    Hi, I have been asked to solve the following equation:
    y'' + 2y' +5y = 0 with the initial conditions y(0) = -1, y'(0) = 1+2*sqrt(3)
    In the form Y(x) = A*e^kx*cos((omega)x - (phi)) Where A is a constant, k is the real root of the auxillary equation, and (omega) is the imaginary part of the root of the auxillary equation.
    Thus far I have solved the axillary equation, used Eulers formula and worked out the necessary constants from the given conditions to get the equation in the form:
    y(x) = e^(-x)*(-cos(2x)+sqrt(3)sin(2x))

    I just wondered if anyone could give me any pointers on how to get from this form of the solution to the one required. Thanks in advance, Kam.

    if what you have got so far is correct:

    compare -cos(2x)+rt(3)sin(2x) with Rcos(2x-phi)=Rcos(phi)cos(2x)+Rsin(phi)s in(2x)

    comparing gives values for Rcos(phi) and Rsin(phi).which can be used to find R and phi
    • Thread Starter

    Ok, I'll try that, thank you for your help.
Submit reply
Turn on thread page Beta
Updated: January 27, 2010
Do you like carrot cake?
Useful resources

Make your revision easier


Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here


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