# Solve dt/dx=(at+m)/(bt+j)

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• Apr 10th 2011, 05:57 PM
Taurus3
Solve dt/dx=(at+m)/(bt+j)
how do I solve dt/dx=(at+m)/(bt+j) where a, b, m, and j are constants?

I thought of using separable equations but then I got stuck.

(So bt+j/at+m)dt=dx....
• Apr 10th 2011, 06:20 PM
topsquark
Quote:

Originally Posted by Taurus3
how do I solve dt/dx=(at+m)/(bt+j) where a, b, m, and j are constants?

I thought of using separable equations but then I got stuck.

(So bt+j/at+m)dt=dx....

$\displaystyle \displaystyle \frac{dt}{dx} = \frac{at + m}{bt + j}$

Basically you need to do the integral:
$\displaystyle \displaystyle \int \frac{bt + j}{at + m}~dt$

Split up the fraction:
$\displaystyle \displaystyle = \int \left ( \frac{bt}{at + m} + \frac{j}{at + m} \right ) dt$

$\displaystyle \displaystyle = \frac{b}{a} \int \frac{t}{t + \frac{m}{a}} dt + \frac{j}{a} \int \frac{1}{t + \frac{m}{a}} dt$

Can you take it from here?

-Dan
• Apr 10th 2011, 08:37 PM
Taurus3
ummm.....it's still a bit confusing of how you do the integrals with all those different constants...
• Apr 10th 2011, 10:44 PM
mr fantastic
Quote:

Originally Posted by Taurus3
ummm.....it's still a bit confusing of how you do the integrals with all those different constants...

Then make the integrals like simpler by substituting $\displaystyle \displaystyle k = \frac{m}{a}$. If you're studying differential equations you're expected to know how to integrate!

If you need more help please show all your working and say where you are stuck.