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Solving differential equations

  1. Dec 6, 2011 #1
    1. The problem statement, all variables and given/known data


    Solve the following differential equation:

    f"(x)=sinx

    x(0)=0, x'(0)=1

    2. Relevant equations

    x(0)=0, x'(0)=1

    3. The attempt at a solution


    f"(x)=sin(x)
    integrate,
    f'(x)=-cos(x)+C1
    f'(0)=-cos(0)+C1=1 => C1=2
    C1=2
    f'(x)=-cos(x)+2
    f(x)=-sin(x)+2x+C2
    f(0)=-sin(0)+C2=0 => C2=0

    =>
    f(x)=-sin(x)+2x
     
  2. jcsd
  3. Dec 6, 2011 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    It is correct.

    ehild
     
  4. Dec 7, 2011 #3

    Mark44

    Staff: Mentor

    Minor point, but this should be f(0) = 0, f'(0) = 1.
    What's your question?
     
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