 In this video, we provide the solution to question number one for practice exam number three for math 1220 We're given a function y equals five minus C e to the negative x and we're supposed to determine which of the following six differential equations is this the solution of now one way to do it is just of course just to start computing and see which One solves each one, you know, you plug it in and see what happens now You'll notice that with each of these possible answers. There are some similarities here There's always like a y plus or minus of five We have to compare it to the Derivative so let's actually compute the derivative first dy over dx see what happens so computing the derivative here y prime is Equal to well you take the derivative of five. It's going to go to zero here Derivative e to the x by the chain rule a negative sign is going to come out So you're going to get a positive C e to the negative x like so so the derivative Notice the fives going to go away the negative sign is going to go away And so I'm going to look for something that actually seems to make that work because after all this is equal to Because if you take y for example, and you times y by negative one Take a negative one there that'll give you a positive C e to negative five But you'll have this extra negative five that's present So if I add five to that or write that as five minus y We then can see that when we put all together the derivative of our function y is equal to five minus y For which then B would be the correct answer. So that way we didn't have to go through every possibility We are able to construct it by actually looking at the general the possible answers and actually see which one's the most correct one