Mathematics
OpenStudy (anonymous):

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

OpenStudy (jamesj):

What methods do you have in your toolbox?

OpenStudy (jamesj):

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

OpenStudy (anonymous):

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

OpenStudy (jamesj):

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

OpenStudy (anonymous):

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

OpenStudy (jamesj):

No, that only works when the coefficients are constants.

OpenStudy (jamesj):

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

OpenStudy (anonymous):

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

OpenStudy (jamesj):

No, usually it means all solutions. I would ask your tutor/lecturer/TA what method you are supposed to use here.

OpenStudy (jamesj):

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

OpenStudy (jamesj):

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

OpenStudy (anonymous):

OpenStudy (jamesj):

Do you know Laplace transforms?

OpenStudy (anonymous):

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.

OpenStudy (jamesj):

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/

OpenStudy (anonymous):

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