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Math Help - solution interval for IVP

  1. #1
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    solution interval for IVP

    Find an interval centered about x=0 for which the given IVP has a unique solution:

    y" + (tan x)y=e^x y(0)=1, y'(0)=0


    How would I find the interval?
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  2. #2
    MHF Contributor chisigma's Avatar
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    Let's write the DE as...

    \cot x\cdot y^{''} + y = e^{x}\cdot \cot x , y(0)=1 , y^{'} (0)= 0 (1)

    Now we remember that necessary condition to have one and only one solution in an interval of the x variable is that the coefficient of the term y^{''} doesn't vanish in that inteval, so that it exists one and only one solution of (1) for -\frac{\pi}{2}<x<\frac{\pi}{2}...

    Kind regards

    \chi \sigma
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  3. #3
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    Thanks!

    Thank you so much, I understand!
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