Ans 1

a. We simply need to subtract

7x dx

from both sides, then insert integral signs and integrate:

NOTE 1: We could have written it in a more familiar way as:

Then So

NOTE 2: $\int dy$ means $\int 1~dy$ . We also have:

and so on.

b. We now use the information y(0) = 3 to find K.

The information means that at x = 0, y = 3. We substitute these values into the equation that we found in part (a), to find the particular solution.

gives K = 3.

So the particular solution is:

Here is the graph of our solution.