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Need Help Solving Initial Value Differential Equation

  1. Sep 3, 2008 #1
    1. The problem statement, all variables and given/known data

    dy/dx + y*cos(x) = 3*cos(x) . Find the particular solution of the differential equation dy/dx + y*cos(x) = 3*cos(x) satisfying the initial condition y(0)=5.

    y(x) = ________________________

    2. Relevant equations

    3. The attempt at a solution

    I thought I had done it the right way, but my computer based homework system disagreed.
    Heres my work:


    m: mu

    m(t)=exp [int] cos(x)dx
    m(t)= e^sin(x)


    e^sinx(y)= [int]3cosx(e^sinx)dx

    [int]3cosx(e^sinx)dx= 3(e^sinx)+C

    then to solve for y,
    y= 3(e^sin(x)+C)/(e^sin(x))

    using the intial value to solve for C, [[the initial value was y(0)=5]]
    5e=3e + C<<<right here is it C or 3c?>>

    and plugging it back into the y-equation, I get y=(3(e^sinx)+2e)/(e^sinx)

    Where have I gone wrong? My homework system says this is wrong... Any help would be greatly appreciated. Thank you for looking.
  2. jcsd
  3. Sep 3, 2008 #2


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    Science Advisor
    Homework Helper

    sin(0)=0 and e^(0)=1 not e.
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