# Linear first order differential equation

• Jul 18th 2012, 04:39 PM
katrina1110
Linear first order differential equation
Hi All

I'm struggling with the linear first order differential equation below. This is from a journal paper, and I'm trying to replicate the results they found. I'm trying to solve for hi with respect to s.

��ℎ��/����=К/���� ����((����.����−1+ℎ��.����)/(����+����)-hi) where all but hi, s and xi are known.

I've tried using the product rule and I get:

ℎ��=����−���� *��^(−0.679.��)

But it doesn't match the results in the paper. When I type it into my graphic calculator, I get a totally different solution:

hi= (s.xi) / (s+1.47)

I would be very grateful for any help on this!

Thanks
• Jul 18th 2012, 05:21 PM
pickslides
Re: Linear first order differential equation
The equation is not clear form your post.
• Jul 18th 2012, 05:33 PM
katrina1110
Re: Linear first order differential equation
Sorry pickslides, the equation is:

dh/ds= (C / A) . t . [((k.x+h.t) / (k+t))-h]