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Math Help - simple pde finding parametric representation with characteristic method

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    simple pde finding parametric representation with characteristic method

    Hello,

    I need to find parametric representation for part d.


    dr/dt + r*dr/dx = -xr
    Here is what I did but I keep not getting good answer

    dx/dt = r
    dr/dx = -x*r = exp(-xt)

    since at t = 0; characteristic x = ct + xo we have  x = xo

    dx/dt = r(xo, 0)*exp(-xt)

    To find x I integrate from zero to t;

    I get: x = r(xo,0)*[(1/x)*exp(-xt)] + xo

    but here's the problem my solution is not xo for t = 0

    Can someone please please help me
    Attached Thumbnails Attached Thumbnails simple pde finding parametric representation with characteristic method-capture.jpg  
    Last edited by boris; January 23rd 2013 at 02:16 AM.
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