I've been trying to solve this problem for quite a while now but can't seem to get the right answer. please any pointer will be greatly appreciated.

A tank contains 50 kg of salt and 1000 L of water. A solution of a concentration 0.025 kg of salt per liter enters a tank at the rate 7 L/min. The solution is mixed and drains from the tank at the same rate.

Find the amount of salt in the tank after 2.5 hours.

Find the concentration of salt in the solution in the tank as time approaches infinity.

my dy/dt equation looks like this dy/dt = .175-7y/1000

after doing the steps my book shows I end up with a really long equation that doesn't help at all.
I know that y(0)=80 kg has to help me find c but the answer is totally wrong. I don't know where did I messed up. Please help.

Easiest way to address stuff like this is replace the numbers with letters and put the numbers back in afterwards. So you get dy/dt = a - by/d which indeed is separable and should give you a solution involving exponentials. Yes it will be a bit messy (these revolting things are). Take it slowly, do it neatly, works for me every time.

__________________
"No matter how fast or how far you run, you're still in the space where you are." -- Russell

I tried but i made a mess and didn't come up with the right equation. :b
what really messes me up it's that extra 7y.

can someone help me figure out the equation with respect to y. please I really need to see what steps I messed up. Thanks.

The DE can be re-written as



subject to the boundary condition y(0) = 50 (or is it 80??).

If you're solving differential equations then it's expected that you can integrate things like with respect to y.

__________________
There are two things you should never try to prove: the impossible and the obvious.

The greater danger for most of us lies not in setting our aim too high and falling short; but in setting our aim too low and achieving our mark. (Michelangelo Buonarroti)

• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  

I know how to get there but after I try to find c(which is y(0)=50). I end up with this equation:

-1/7 ln(175-7y)= t/1000 + c

my c= -1/7ln(-175)

leaving

-1/7 ln(175-7y)= t/1000 -1/7ln(-175)

from here is where I mess something up and cannot find the answer.

My advice is to get y in terms of t before using the boundary condition:



note the use of absolute value | | NOT () ......



where is just as arbitrary as

.

Now substitute y = 50 (80??) when t = 0 and solve for A.

__________________
There are two things you should never try to prove: the impossible and the obvious.

The greater danger for most of us lies not in setting our aim too high and falling short; but in setting our aim too low and achieving our mark. (Michelangelo Buonarroti)

• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.