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Variation of Parameters, system of equations

  1. Mar 15, 2010 #1
    1. The problem statement, all variables and given/known data
    y''+25y=cot(5x)
    Find one possible solution


    3. The attempt at a solution
    I don't have any background in linear algebra, so I can't use cramers rule as a heads up, so I have to solve the system of equations (no linear algebra for this course is needed).

    Ok, so I take the auxiliary, r^2=-25, r=+/-5i

    y_h=Acos(5x)+Bsin(5x)

    y_1=cos(5x) y_2=sin(5x)

    Then,
    u_1'cos(5x)+u_2'sin(5x) = 0
    -5u_1'sin(5x)+5u_2'cos(5x) = cot(5x)

    I am stumped at how to solve this system of equations. I think the rest before it is right..?

    Seems like the algebra has got me.
     
  2. jcsd
  3. Mar 16, 2010 #2
    Perhaps I'm going about this completely wrong then. How would I start out solving y''+25y=cot(5x).

    (I should be more specfic, when I say solve, I mean to find A solution, so y_h and y_p. I'm just not sure about how to find the y_p=u1(y_1)+u2(y_2))
     
  4. Mar 16, 2010 #3

    rock.freak667

    User Avatar
    Homework Helper

    u1' = -u2'tan(5x), sub that into the other equation.

    this may help you as well sin2x+cos2x=1

    Though, you could just use the direct result to make this easier. You are sure you can't use the Wronskian?
     
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