So I have the following differential equation.
The general solution I have is:
t=k(-1/r)+c
I now need to find the particular solution when t=0 and the radius (r) = 1cm.
So k is a constant which is approx 3.9 (5/4pi)
So for the particular solution im really just plugging in the numbers to find the value of c, is that correct?
Thanks
Just to add, by doing what I described above my answer for c would be the same value as for k (i.e 3.9 or 5/4pi) so my particular solution would be.
t=k(-1/r)+5/4pi
yes, c=k, so if k = 5π/4,
t = k (1 - 1/r)
= 5π/4 (1 - 1/r)
Thanks Steve.
Yes, you're on the right track. To find the particular solution, you need to plug in the given values of t and r into the general solution and solve for the constant c.
In this case, you are given t = 0 and r = 1 cm. Substituting these values into the general solution, you get:
0 = k(-1/1) + c
Since you already know the value of k is approximately 3.9 (5/4π), you can substitute it in:
0 = 3.9(-1) + c
Now, you can solve this equation to find the value of c:
0 = -3.9 + c
To isolate c, you add 3.9 to both sides:
c = 3.9
Therefore, the particular solution when t = 0 and r = 1 cm is:
t = k(-1/r) + c = 3.9(-1/1) + 3.9 = -3.9 + 3.9 = 0
Hope this helps! Let me know if you have any further questions.