y remains finite for large values of x

Hi again, just a quick question about the wording of a question.

I have the General Solution to a differential equation:

We are given the fact that when , .

From this fact I've got the equation

The only other information we are given is that y remains finite for large values of x.

Here's how I interpreted this, can someone please just verify that this is right.

When is large, then tends towards 0, we can then discount this from out equation.

When gets larger, eventually goes towards infinity, but the question states that y remains finite, therefore .

The final solution I have got then is:

.

Is this correct?

Thanks