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Math Help - Seperable Differential EQ

  1. #1
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    Seperable Differential EQ

    The question is

    \frac{du}{dr} = \frac {1+\sqrt{r}}{1+\sqrt{u}}


    And I am supposed to solve for u.

    The answer I got was

    u + \frac{2\sqrt{u^3}}{3} = r + \frac{2\sqrt{r^3}}{3} + C

    Is there a way I can solve for u?
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  2. #2
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    Hello,

    Is there an initial condition so that you can get C ?

    Because if C is 0, I have this factorisation :

    (\sqrt{u}-\sqrt{r})\left(\frac 23 \cdot u+\frac 23 \sqrt{ur}+\frac 23 \cdot r+\sqrt{u}+\sqrt{r}\right)=0

    Since you talked about \sqrt{r} and \sqrt{u}, we can assume that u and r are positive.

    Thus the solutions are : u=r, or u=r=0 (for the second term, because it's always \geq 0)
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  3. #3
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    C is just the arbitrary constant associated with the integration. But it isn't given a value so it needs to be in the final equation.
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