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Math Help - Find all functions u_0(x)...

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

    Find all functions u_0(x) for which the problem

    u_x-2u=0

    u(x,0)=u_0(x)

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

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

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

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

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