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....

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- Apr 10th 2011, 05:57 PMTaurus3Solve 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 PMtopsquark
$\displaystyle \displaystyle \frac{dt}{dx} = \frac{at + m}{bt + j}$

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 PMTaurus3
ummm.....it's still a bit confusing of how you do the integrals with all those different constants...

- Apr 10th 2011, 10:44 PMmr fantastic