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Math Help - Find the general solution for the differential equation

  1. #1
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    Find the general solution for the differential equation

    dy/dx - 2y.cosecx=tan(x/2) between 0<x<pi

    Having some trouble with this one - I have taken e^integral of 2cosecx - which I got (tan(x/2))^2 - Then I multiplied this to all terms and I am not sure if what I'm getting is working so a full explanation would be really appreciated.

    Many thanks,

    Bryn
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  2. #2
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    Quote Originally Posted by Bryn View Post
    dy/dx - 2y.cosecx=tan(x/2) between 0<x<pi

    Having some trouble with this one - I have taken e^integral of 2cosecx - which I got (tan(x/2))^2 - Then I multiplied this to all terms and I am not sure if what I'm getting is working so a full explanation would be really appreciated.

    Many thanks,

    Bryn
    Close ..... you need e^{\int {\color{red}-}2 \, \text{cosec} \, x \, dx}.

    So the integrating factor will be \frac{1}{\tan^2 \frac{x}{2}}.
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