Solving dm/ds = m with initial condition m(1) = 7

[nick.martinez]

dm/ds=m ; m(1)=7

when i find the diff eq

∫dm/m=∫ds

ln|m|+c1=s+c2 ; k=c2-c1

ln|m|=s+k
e ^ both sides

m(s)=e^(s+k) ; m(1)=7

m(1)=e^(1)*e^(k)=7
i am stuck here. not sure how to proceed please help.

 

[DeeAytch]

What are you trying to figure out with your initial condition?

Can you solve this equation using another technique?

 

[HallsofIvy]

dm/ds=m ; m(1)=7

when i find the diff eq

∫dm/m=∫ds

ln|m|+c1=s+c2 ; k=c2-c1

There is really no need to write both c1 and c2. It's perfectly proper to immediately combine the two "constants of integration" to write ln|m|= s+ k.

ln|m|=s+k
e ^ both sides

m(s)=e^(s+k) ; m(1)=7

m(1)=e^(1)*e^(k)=7
i am stuck here. not sure how to proceed please help.[/QUOTE]
So e^k= 7e^{-1}.

e^(s+k)= e^k e^s so m(s)= 7e^{-1}e^k or m(s)= 7e^(k-1).