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Math Help - a mess of a diff eq

  1. #1
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    a mess of a diff eq

    almost got a solution to a differential equation, but wondering if anyone could help me tidy things up...

    I have (int 1/(1+v^2)dv - (int v/(1+v^2)dv = ln(x)+C

    which gives

    arctan(v)-1/2ln(1+v^2)=ln(x)+C

    Iam using v=y/x

    is there any way of solving for y?? I thought of using exp but itll probz end up messy, what would be the general solution in this case?

    another prob if anyones up for it,
    an integral left from a dif eq...

    int 1+v/((v-1)^2) dv .....
    Last edited by dankelly07; March 6th 2008 at 04:01 PM.
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by dankelly07 View Post
    almost got a solution to a differential equation, but wondering if anyone could help me tidy things up...

    I have (int 1/(1+v^2)dv - (int v/(1+v^2)dv = ln(x)+C

    which gives

    arctan(v)-1/2ln(1+v^2)=ln(x)+C

    Iam using v=y/x

    is there any way of solving for y?? I thought of using exp but itll probz end up messy, what would be the general solution in this case?

    another prob if anyones up for it,
    an integral left from a dif eq...

    int 1+v/((v-1)^2) dv .....
    I don't think it can be solved for y...

    As for your integral

    \frac{v+1}{(v-1)^2}=\frac{v-1+2}{(v-1)^2}=\frac{1}{v-1}+\frac{2}{(v-1)^2}

    This should help...
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