Question

Initial Value Problem

Answer 1

\[\frac{ dy }{ dt }=-y+5\]
with initial value \[y(0) = y_{0}\]

Answer 2

dy
-- = dt
5 - y

integrating

ln (5 - y) = t + C

5 - y = e ^(t + C)

y = 5 - Ae^t

Answer 3

the back of the book has \[y=5t(y _{0}-5)e ^{-t}\]
as the answer

Answer 4

thats solved the equation but i;m not clear about the y(0) part - i've just started doing these in university

Answer 5

sorry - I'm not sure about this

Answer 6

kk no problem, i got to the part where u got and then didnt know what to do