I don't think you are given enough information to solve it completely,
for you are not given any initial conditions. You'd need more than you're
given for there is no way to know what the constant of proportionality k
would be. I'll do what I can. But I hit a dead end.
The differential equation comes from these words:
the rate of net investment (the rate of change of the total capital invested)
should be proportional to the difference between C and the total capital
invested
Multiply through by dt:
divide through by C-y
Integrate both sides
Change to exponential form:
is just another constant c2
Nothing else is given except
the level of its investment should not exceed C
We have no more information to get rid of those constants.
Sorry, that's as far as I can go with it.
Edwin