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Math Help - first order ODE, Fresnel integral?

  1. #1
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    first order ODE, Fresnel integral?

    for this ODE- \frac{dy}{dt}+y\sqrt{t}sint=0, do I need to use a Fresnel integral to solve it? or can it be simplified another way from the standard form y(t)=cexp(-I)? it can be expanded to the expression- \large y(t)=ce^{\sqrt{2}cost+\frac{1}{2}\int \frac{cost}{\sqrt{t}}dt}

    thanks very much!
    Last edited by mathlover10; April 20th 2013 at 04:12 PM.
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  2. #2
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    Re: first order ODE, Fresnel integral?

    Hey mathlover10.

    You should be able to use an integrating factor or a simple separation of variables to solve this DE.
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  3. #3
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    Re: first order ODE, Fresnel integral?

    Hi mathlover10 !
    Any method used to solve the ODE will not change the result. If one method leads to a Fresnel integral, do not expect something else from another method.
    If you don't want a closed form, such as a Fresnel integral, it's up to you to search an infinite series instead of.
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