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Math Help - differential equations

  1. #1
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    differential equations

    Can anyone help me with this

    cos(^2)x.(dy/dx) +y = tanx

    i followed the general way but i can't integrate tanxsec^2x.e^tanx

    thanks
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  2. #2
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    Quote Originally Posted by Dili View Post
    Can anyone help me with this

    cos(^2)x.(dy/dx) +y = tanx

    i followed the general way but i can't integrate tanxsec^2x.e^tanx

    thanks
    Let tanx=u, then integrate (ue^u)du
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  3. #3
    Math Engineering Student
    Krizalid's Avatar
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    Quote Originally Posted by Dili View Post
    i followed the general way but i can't integrate tanxsec^2x.e^tanx
    Add & subtract e^{\tan{x}}\cdot\sec^2x

    Then group some terms to turn the integrand into a product's function derivative.

    The general solution to your differential equation is \color{blue}y=k\cdot{e}^{-\tan{x}}+\tan{x}-1,~~k\in\mathbb{R}
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