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

• Sep 21st 2011, 04:25 PM
coolsheep
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.

• Sep 21st 2011, 04:31 PM
pickslides
Re: Simplifying an equation containing both a first order and second order differenti
You have $zy''= ty'+r$

so $zy''-r= ty'$

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

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?
• Sep 21st 2011, 04:37 PM
coolsheep
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?