# Thread: Solving a differential equation

1. ## Solving a differential equation

I have the following differential equation

$\displaystyle \frac{\partial}{\partial t}\left(\frac{a}{X}\right)+\frac{X}{b}\frac{\parti al Y}{\partial t}+\frac{c}{X}=0$

where $\displaystyle a$, $\displaystyle b$ and $\displaystyle c$ are constants and $\displaystyle X$ is a function of
$\displaystyle t$. I want to solve it for $\displaystyle Y$ analytically (if possible) or numerically.

Note: the second term is $\displaystyle \frac{X}{b}\frac{\partial Y}{\partial t}$.

2. ## Re: Solving a differential equation

Hey JulieK.

The first hint I would suggest is to multiply both sides by X. Also is Y independent of X and t?

3. ## Re: Solving a differential equation

Hi Chiro

Many thanks!
What is the advantage of multiplying both sides by X.
Y is dependent on both X and t.

By the way, I obtained the following relation which may help to find a solution

$\displaystyle Y=\frac{d}{O}\left(X^{1/2}-O^{1/2}\right)$

where $\displaystyle d$ is a constant and $\displaystyle O$ is a known function of $\displaystyle t$ with
a closed analytical form.

4. ## Re: Solving a differential equation

With regard to the hint, you might want to try differentiating your hint function and then compare this to the structure of the DE to obtain the O function.