Thread: Slope Field Help?

Here's the problem:

At any point of intersection of a solution curve of the d.e. y'=x+y and the line x+y=0, the function y at that point
(a) is equal to 0
(b) is a local maximum
(c) has a local minimum
(d) has a point of inflection
(e) has a discontinuity

First, what does "d.e." mean? Derivative?
Second, I have no clue how to figure this out, so any help would be much appreciated!

Originally Posted by summermagic

Here's the problem:

At any point of intersection of a solution curve of the d.e. y'=x+y and the line x+y=0, the function y at that point
(a) is equal to 0
(b) is a local maximum
(c) has a local minimum
(d) has a point of inflection
(e) has a discontinuity

First, what does "d.e." mean? Derivative?
Second, I have no clue how to figure this out, so any help would be much appreciated!

DE = Differential Equation.

Originally Posted by summermagic

Here's the problem:

At any point of intersection of a solution curve of the d.e. y'=x+y and the line x+y=0, the function y at that point
(a) is equal to 0
(b) is a local maximum
(c) has a local minimum
(d) has a point of inflection
(e) has a discontinuity

First, what does "d.e." mean? Derivative?
Second, I have no clue how to figure this out, so any help would be much appreciated!

The d.e. y'=x+y can be solved using the intergrating factor method.

Integrating factor - Wikipedia, the free encyclopedia

I tried this and got an integrating factor of exp(-x)

You can also maybe use the fact that y'=x+y and x+y=0

implies y' = 0