integration of summed term

[camxg1977]

Hi,
I'm struggling to integrate the following equation which is a simplified kinetic expression which shows how the concentration of a material B changes with time t.
How do I get it into a form that can be integrated and which integration method should be used?

d+ dt = exp(-kt)dt

 

[topsquark]

Is this supposed to be dB = exp(-kt) dt? The expression d + dt makes no sense.

-Dan

 

[Dr.Peterson]

Hi,
I'm struggling to integrate the following equation which is a simplified kinetic expression which shows how the concentration of a material B changes with time t.
How do I get it into a form that can be integrated and which integration method should be used?

d+ dt = exp(-kt)dt

Can you show the original problem you are working on, ideally as an image showing exactly how this was written, or what larger problem it comes from?

 

[camxg1977]

The B's did not paste in the original query. Apologies. The correct form is below.
dB+ Bdt = exp(-kt)dt

 

[topsquark]

The B's did not paste in the original query. Apologies. The correct form is below.
dB+ Bdt = exp(-kt)dt

"Dividing" by dt you get
[imath]B'(t) + B(t) = e^{-kt}[/imath]

a first order DEq. You need to find the homogeneous solution and a particular solution. Can you do that?

-Dan

Addendum: Or you could use an integrating factor if that's how to learned how to do these.

 

[camxg1977]

I am still struggling here I am afraid. I've not come across integrating factors either.

 

[Deleted member 4993]

I am still struggling here I am afraid. I've not come across integrating factors either.

Homogeneous part is :

B'(t) +B(t) = 0

What is the solution for that D.E. ?

Most of us would like to see your response to post #3.