# Solve this ordinary differential equation if you can

Hi everyone!

Thank you.

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#### SlipEternal

MHF Helper
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.

2 people

#### Ekram

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

Thank you.

#### Walagaster

MHF Helper
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?

1 person

#### Vinod

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 $-2b\arctan{(\frac{y}{b})}+y+C$=$-a\ln{(|a-x|)}+a\ln{(|a+x|)}-x+C$