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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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  4. #4
    Member Walagaster's Avatar
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    Re: Solve this ordinary differential equation if you can

    Edit: Dang! I just noticed how old this thread was. Never mind.

    We aren't here to do your homework for you. But I do have some suggestions for you:
    1. Don't post sideways images.
    2. Don't post images anyway. Type them. That way we can edit your work with suggestions or corrections.
    3. Post each problem in a separate thread, showing what you have tried. Do you seriously think anyone is going to post solutions to 30 problems for you?
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  5. #5
    Senior Member Vinod's Avatar
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    Re: Solve this ordinary differential equation if you can

    Quote Originally Posted by SlipEternal View Post
    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.
    Hello,
    I got the answer from my integral calculator $-2b\arctan{(\frac{y}{b})}+y+C$=$-a\ln{(|a-x|)}+a\ln{(|a+x|)}-x+C$

    What is the difference between your answer and my answer?
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