Inital Value Theorem ??

[MHENK]

I know that if y'=ky and y(o)=A, then y=Ae^kt. But in the following problem, I am given y(10), not y(0). How would I go about solving this to get an equation for y?

y'=ky
y(10)=2y(0)

Thanks in advance,

MHENK

[Shaunak]

ln y = kx + c
where c is some constant
given y(10) = 2y(0)
therefore
e^(10k + c) = 2e^(c)
=>k = (ln 2)/10
the solution is therefore
y = x(ln 2)/10 + c
where c is some real const