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....
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