1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Second Order Differential Equations

  1. Oct 30, 2007 #1
    1. The problem statement, all variables and given/known data
    Consider the second order differential equation y'' - 4y' + 4y = f(x)
    Find a particular solution if f(x) = 25cos(x)

    2. Relevant equations
    I believe for this type of question I should let y = Asin(x) + B cos(x)
    Hence y' = Acos(x) - Bsin(x) and
    y'' = -Asin(x) - Bsin(x)

    3. The attempt at a solution
    I think everything above is right, and for the rest of the question I should just be able to substitute back into the original formula and find values for A and B.
    The problem is when I do substitute back in all I get is a mess and a headache!

    Here is what I got by substitution:
    -Asin(x) - Bcos(x) - 4[Acos(x) - Bsin(x)] + 4[Asin(x) + Bcos(x)] = 25cos(x)
    Hence
    -Asin(x) + 4[Asin(x) + Bsin(x)] - Bcos(x) - 4[Acos(x) - Bcos(x)] = 25cos(x)

    That's about all I think I can do and I have no idea how to obtain values for A and B. I know the answer is y(p) = 3cos(x) - 4sin(x).
    How to get this answer from the above I have no idea, I'm obviously missing something.
    Thanks in advance for any advice or help.
     
  2. jcsd
  3. Oct 30, 2007 #2

    Integral

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    You are just about there. Gather your sinx terms then factor the sin, same for the cosx terms, now, since sin x does not appear in the particular solution set its coefficient to zero, solve for A in terms of B. Set the coefficient for the cos x term = 25 and find B.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Second Order Differential Equations
Loading...