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Thread: Find all functions u_0(x)...

  1. #1
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    Find all functions u_0(x)...

    Find all functions $\displaystyle u_0(x)$ for which the problem

    $\displaystyle u_x-2u=0$

    $\displaystyle u(x,0)=u_0(x)$

    $\displaystyle \displaystyle\int\frac{u_x}{u}dx=\int 2dx\Rightarrow \ln|u|=2x+g(y)$

    $\displaystyle u(x,y)=\varphi(y)\exp{(2x)}$

    $\displaystyle u(x,0)=\varphi(0)\exp{(2x)}=u_0(x)$

    How is $\displaystyle \varphi(0)$ handled in this situation?

    Thanks.
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  2. #2
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    Assuming that $\displaystyle \varphi(0)$ is defined, it will just be a constant.
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