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Math Help - showing existence of nontrivial solution

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    showing existence of nontrivial solution

    Show that the differential equation x' = \frac{x \sin(e^x+t)}{1+(e^t \cos x+x)^2}, x(1) = 1 has a nontrivial solution \phi(t) defined on
    [0,2] such that 0 < \phi(t) < \frac{\pi}{2} for all t \in [0,2].

    I only know that x = 0 is a trivial solution. Then how do I proceed?
    Last edited by alphabeta89; November 7th 2012 at 04:14 AM.
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