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Math Help - graphing problem

  1. #1
    Junior Member
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    graphing problem

    I have a question for a problem in my homework. I was given the following differential equation

    \frac{dr}{d\theta} =  \frac{r^2}{\theta} <br /> <br />

    r(1) = 2

    When i solved the equation I get

    \frac{1}{ln\theta} =  r<br /> <br />

    My question is how do I go for solving for c? I know to just plug in 2 for r and 1 for theta. Is this problem in polar form? I have not covered polar form in any of my classes so that is where I think I am lost. any help would be appreciated.
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  2. #2
    MHF Contributor alexmahone's Avatar
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    \frac{dr}{d\theta} = \frac{r^2}{\theta}

    \frac{dr}{r^2}=\frac{d\theta}{\theta}

    Integrating both sides,

    -\frac{1}{r}=ln \theta+C ------ (1)

    r(1)=2

    Substituting in (1) we get,

    -\frac{1}{2}=ln 1+C

    C=-\frac{1}{2}

    Hence,

    -\frac{1}{r}=ln \theta-\frac{1}{2}
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