Question

Could someone please help me to solve the following differential equation?
y" + (x+2)y' + (1+x)y = 0

Answer 1

What methods do you have in your toolbox?

Answer 2

I would solve this with a Laplace transform. Do you have that?

Answer 3

Yes, Is there a method using integrating factor? I think it comes under that section.Thanks.

Answer 4

The other thing to observe is that one solution can be deduced by inspection:
y = Ae^(-x)

Answer 5

Can I use the characterictic equation to solve this? where the roots are - (x+1) and -1 or am I in the wrong direction?

Answer 6

No, that only works when the coefficients are constants.

Answer 7

Are you asked for the complete solution? Or just a solution?

Answer 8

The question is to 'Solve the this equation so I guess it is just a solution.

Answer 9

No, usually it means all solutions.

I would ask your tutor/lecturer/TA what method you are supposed to use here.

Answer 10

I would be interested in seeing a solution which didn't use Laplace transforms, if you find out.

Answer 11

For the record, here is the general solution:
http://www.wolframalpha.com/input/?i=y%22+%2B+%28x%2B2%29y%27+%2B+%281%2Bx%29y+%3D+0

Answer 12

Would you please post the answer using Laplace transform?

Answer 13

Do you know Laplace transforms?

Answer 14

Can't remeber much about it, I have that in my course though. This assignment is before I cover that section, I think. I am doing this as a reading paper not sure if I can use it or not.

Answer 15

Well, there's really not a great point in showing you the Laplace transform solution if you won't understand it.

But if you want to understand the basics of that method, I would refer you to these excellent lectures, beginning here:
http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/lecture-19-introduction-to-the-laplace-transform/

Answer 16

I think so too. I will have look at this site. Thanks so much for help. Appreciate it.