Thread: where does he get this term from?

I have the differential equation

dT/ds = C + BT

which is derived from

dT = Fds, F = umg + (1/2)CrAv^2, v^2 = 2T/m

and where

T = Kinetic energy
s = distance
C and B are constants

I have been shown a solution

(1/B)*ln(C+BT) = s + D

I understand that he has done the integral of;

dT/(C+BT) = ds

but how does he get the above result?

integral of 1/x = ln(x)

Where does the 1/B come from.

The solution he provoded does not match with my numerical solution.

Any help would be greatly appreciated

Originally Posted by revolution2000

I have the differential equation

dT/ds = C + BT

which is derived from

dT = Fds, F = umg + (1/2)CrAv^2, v^2 = 2T/m

and where

T = Kinetic energy
s = distance
C and B are constants

I have been shown a solution

(1/B)*ln(C+BT) = s + D

I understand that he has done the integral of;

dT/(C+BT) = ds

but how does he get the above result?

integral of 1/x = ln(x)

Where does the 1/B come from.

The solution he provoded does not match with my numerical solution.

Any help would be greatly appreciated

To integrate if you use the substitution then and your integral becomes