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Thread: Solve this ordinary differential equation if you can

  1. #1
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    Solve this ordinary differential equation if you can

    Hi everyone!

    Can you please help me solve this ordinary differential equation in the attachment below?


    Thank you.
    Attached Thumbnails Attached Thumbnails Solve this ordinary differential equation if you can-img_e3027.jpg  
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  2. #2
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    Re: Solve this ordinary differential equation if you can

    This is a separable ODE.

    $\dfrac{y^2-b^2}{y^2+b^2}dy = -\dfrac{x^2+a^2}{x^2-a^2}dx$

    $y-b\arctan\left(\dfrac{y}{b}\right) = -x-2\int\left(\dfrac{a^2}{x^2-a^2}\right)dx = -x-2a\text{tanh}^{-1}\left(\dfrac{x}{a}\right)+C$

    The final integral can be split up using Partial Fractions if you do not like inverse hyperbolic functions.
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  3. #3
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    Re: Solve this ordinary differential equation if you can

    Solve this ordinary differential equation if you can-img_3050.jpgSolve this ordinary differential equation if you can-img_3051.jpgSolve this ordinary differential equation if you can-img_3052.jpg

    I have some of these problems that i am finding hard to solve. can you please provide me the solutions of them?

    Thank you.
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