Results 1 to 10 of 10

Math Help - Solve Differential Equation..Urgent Help Needed

  1. #1
    Junior Member
    Joined
    Jun 2008
    Posts
    44

    Solve Differential Equation..Urgent Help Needed

    Could you please help me with this kind of question?Any respond would be greatly thanks


    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Jun 2008
    Posts
    44
    Quote Originally Posted by noob View Post
    Could you please help me with this kind of question?Any respond would be greatly thanks



    How can i factor the equation??
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Chicago, IL
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by noob View Post
    How can i factor the equation??
    Hint : Expand \bigg(r^2+r+1\bigg)^2...

    --Chris
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Jun 2008
    Posts
    44
    Quote Originally Posted by Chris L T521 View Post
    Hint : Expand \bigg(r^2+r+1\bigg)^2...

    --Chris
    normally as to factorized the equation, i'll use synthetic division, but in that case, i'll not be able to find a single value that satisfying the equation (try and error method)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Jun 2008
    Posts
    44
    Quote Originally Posted by Chris L T521 View Post
    Hint : Expand \bigg(r^2+r+1\bigg)^2...

    --Chris
    is it we get : r^4+2r^3+3r^2+2r+1 ????
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Jun 2008
    Posts
    44
    Quote Originally Posted by Chris L T521 View Post
    Hint : Expand \bigg(r^2+r+1\bigg)^2...

    --Chris

    i've got an imaginary number as their factor

    <br />
(r^2+r+1)^2

    [(-0.5+0.866i)(-0.5-0.866i)]^2

    how can i solved it??i really confused rite now
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Chicago, IL
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by noob View Post
    is it we get : r^4+2r^3+3r^2+2r+1 ????
    Doesn't this look like the Characteristic equation? (It is...)

    Since our C.E. is r^4+2r^3+3r^2+2r+1 , it factored out to \bigg(x^2+x+1\bigg)^2.

    Thus r=\frac{-1\pm\sqrt{1-4}}{2}=\bigg(-\frac{1}{2}\pm\frac{\sqrt{3}}{2}i\bigg) with multiplicity 2...

    Can you find the general solution from here?

    --Chris
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member
    Joined
    Jun 2008
    Posts
    44
    Quote Originally Posted by Chris L T521 View Post
    Doesn't this look like the Characteristic equation? (It is...)

    Since our C.E. is r^4+2r^3+3r^2+2r+1 , it factored out to \bigg(x^2+x+1\bigg)^2.

    Thus r=\frac{-1\pm\sqrt{1-4}}{2}=\bigg(-\frac{1}{2}\pm\frac{\sqrt{3}}{2}i\bigg) with multiplicity 2...

    Can you find the general solution from here?

    --Chris
    is is the general solution lokk like this

    y(x) = c1 e^(1/2 + surd3/2 i ) + c2 e^(1/2 - surd3/2 i)

    the other two factor is what??i might done it wrongly..correct me plese..thanks in advanced
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Chicago, IL
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by noob View Post
    is is the general solution lokk like this

    y(x) = c1 e^(1/2 + surd3/2 i ) + c2 e^(1/2 - surd3/2 i)

    the other two factor is what??i might done it wrongly..correct me plese..thanks in advanced
    Since the conjugate roots are repeated, the general solution takes the form:

    y=c_1e^{-\frac{1}{2}+\frac{\sqrt{3}}{2}i}+c_2e^{-\frac{1}{2}-\frac{\sqrt{3}}{2}i}+c_3xe^{-\frac{1}{2}+\frac{\sqrt{3}}{2}i}+c_4xe^{-\frac{1}{2}-\frac{\sqrt{3}}{2}i}

    However, we don't like to see complex numbers in the solution, so we use Euler's Formula \bigg(e^{i\theta}=\cos(\theta)+i\sin(\theta)\bigg) to clean things up:

    After some calculations, we find that our general solution is:

    y=e^{-\frac{1}{2}x}\left[c_1\cos\left(\frac{\sqrt{3}}{2}\right)+c_2\sin\lef  t(\frac{\sqrt{3}}{2}\right)\right]+xe^{-\frac{1}{2}x}\left[c_3\cos\left(\frac{\sqrt{3}}{2}\right)+c_4\sin\lef  t(\frac{\sqrt{3}}{2}\right)\right]

    \implies \color{red}\boxed{y=e^{-\frac{1}{2}x}\left[\left(c_1+c_3x\right)\cos\left(\frac{\sqrt{3}}{2}\  right)+\left(c_2+c_4x\right)\sin\left(\frac{\sqrt{  3}}{2}\right)\right]}

    To see how we go from y=c_1e^{(\alpha+\beta  i)x}+c_2e^{(\alpha-\beta i) x}\implies y=e^{\alpha x}\left[c_1\cos(\beta x)+c_2\sin(\beta x)\right], read post #3 in my Diff Equ Tutorial.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Junior Member
    Joined
    Jun 2008
    Posts
    44
    Quote Originally Posted by Chris L T521 View Post
    Since the conjugate roots are repeated, the general solution takes the form:

    y=c_1e^{-\frac{1}{2}+\frac{\sqrt{3}}{2}i}+c_2e^{-\frac{1}{2}-\frac{\sqrt{3}}{2}i}+c_3xe^{-\frac{1}{2}+\frac{\sqrt{3}}{2}i}+c_4xe^{-\frac{1}{2}-\frac{\sqrt{3}}{2}i}

    However, we don't like to see complex numbers in the solution, so we use Euler's Formula \bigg(e^{i\theta}=\cos(\theta)+i\sin(\theta)\bigg) to clean things up:

    After some calculations, we find that our general solution is:

    y=e^{-\frac{1}{2}x}\left[c_1\cos\left(\frac{\sqrt{3}}{2}\right)+c_2\sin\lef  t(\frac{\sqrt{3}}{2}\right)\right]+xe^{-\frac{1}{2}x}\left[c_3\cos\left(\frac{\sqrt{3}}{2}\right)+c_4\sin\lef  t(\frac{\sqrt{3}}{2}\right)\right]

    \implies \color{red}\boxed{y=e^{-\frac{1}{2}x}\left[\left(c_1+c_3x\right)\cos\left(\frac{\sqrt{3}}{2}\  right)+\left(c_2+c_4x\right)\sin\left(\frac{\sqrt{  3}}{2}\right)\right]}

    To see how we go from y=c_1e^{(\alpha+\beta  i)x}+c_2e^{(\alpha-\beta i) x}\implies y=e^{\alpha x}\left[c_1\cos(\beta x)+c_2\sin(\beta x)\right], read post #3 in my Diff Equ Tutorial.
    thanks mates..thank you very much..still looking and try to understand the calculation
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Urgent Help needed to solve equation.
    Posted in the Algebra Forum
    Replies: 7
    Last Post: January 11th 2009, 06:05 AM
  2. Urgent: ......differential equation (another).
    Posted in the Calculus Forum
    Replies: 3
    Last Post: February 6th 2008, 06:01 PM
  3. Ordinary Differential equation help needed.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 19th 2007, 03:45 PM
  4. urgent help needed with differential equations
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 2nd 2007, 04:49 AM
  5. Urgent help needed on equation!!!
    Posted in the Algebra Forum
    Replies: 3
    Last Post: April 23rd 2007, 05:25 PM

Search Tags


/mathhelpforum @mathhelpforum