# Thread: Simplifying an equation containing both a first order and second order differential

1. ## Simplifying an equation containing both a first order and second order differential

Hi,

Apologies in advance if this is a simple/stupid question - I am a biologist...

I have an equation of the form:

z . d^2y/dx^2 = t . dy/dx + r

where z, t and r are all constants. I am wondering if there is a simpler way to state this? With the eventual aim of having the equation in the form t = ..... as at the moment I cannot see how t relates to dy/dx as the d^2y/dx^2 is variable.

2. ## Re: Simplifying an equation containing both a first order and second order differenti

You have $\displaystyle zy''= ty'+r$

so $\displaystyle zy''-r= ty'$

$\displaystyle \frac{zy''-r}{y'}= t$

but that would be too simple and is a fucntion of differentials.

Is it fair to guess you need to solve the DE first, then solve for t? Remember t is constant, do you want to make this the subject?

3. ## Re: Simplifying an equation containing both a first order and second order differenti

Ah sorry, t is dependent on dy/dx so it is not constant. I am hoping to be able to make the general statement that assuming z and r are constant, t is proportional to some function of dx/dy. I dont know if this is possible?