solve the differential equation:

u''+u' = 3xExp[-x]+Exp[-x]

I know that since my homogeneous solution has Exp^[-x] in it and so the form of my particular solution needs to be C*x*Exp[-x]... BUT WAIT. the right hand side also has a 3xExp[-x] in it so i guess i need the form of the particular solution to have a x^2*Exp[-x] in it. So is the form of the particular like this? u = A*x^2*Exp[-x]+B*x*Exp[-x]+C*Exp[-x]

Or is it just u=A*x^2*Exp[-x]??

Thanks!

Question

solve the differential equation:

u''+u' = 3xExp[-x]+Exp[-x]

I know that since my homogeneous solution has Exp^[-x] in it and so the form of my particular solution needs to be C*x*Exp[-x]... BUT WAIT. the right hand side also has a 3xExp[-x] in it so i guess i need the form of the particular solution to have a x^2*Exp[-x] in it.  So is the form of the particular like this?  u = A*x^2*Exp[-x]+B*x*Exp[-x]+C*Exp[-x]

Or is it just u=A*x^2*Exp[-x]??

Thanks!

anonymous · Answer

A solution using Mathematica is attached.

anonymous · Answer

Great i appreciate the effort but i'm looking for a by hand solution using method of undetermined coefficients.  Turned out if you do a wolfram alpha query you can look up how to do this using method of undetermined coefficients when i ask for a step by step solution.   I didnt realize it was going to give me this before asking a question.  thanks though.

anonymous · Answer

here is the actual workbook if you like.