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Initial Value Problem

  1. Jul 12, 2007 #1
    1. The problem statement, all variables and given/known data

    Solve the initial value problem for y.


    [tex]y(0)\,=\,a[/tex] & [tex]y\prime(0)\,=\,0[/tex]

    a is a non-zero constant.

    2. Relevant equations

    The calculus.

    3. The attempt at a solution

    [tex]y\prime\,=\,sinh\,x[/tex] [tex]\longrightarrow[/tex] [tex]dy\prime\,=\,cosh\,x\,dx[/tex]



    [tex]\int dy\prime\,=\,\frac{1}{a}\,\int cosh\,x\,dx[/tex]


    C = 0 from the initial condition [itex]y\prime(0)\,=\,0[/itex]

    [tex]\int y\prime\,=\,\frac{1}{a}\,\int sinh\,x\,dx[/tex]





    That doesn’t match the answer that maple gives, what did I do wrong?
    Last edited: Jul 12, 2007
  2. jcsd
  3. Jul 13, 2007 #2

    [tex]dy\prime\,=\,\sqrt{1+y\prime^2}\, dx \,=\,\sqrt{1+\frac{(sinh\,x)^2}{a^2}}\, dx \,\neq\,\frac{1}{a}\,cosh\,x\,dx[/tex]
    Last edited: Jul 13, 2007
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