Find a particular solution to the differential equation y" + 5y' + 6y = 36t^3. Undetermined Coefficients problem

Question

Find a particular solution to the differential equation y" + 5y' + 6y = 36t^3.  Undetermined Coefficients problem

freckles · Answer

the right hand side is a cubic so try a cubiv

freckles · Answer

cubic*

freckles · Answer

$$y_p=At^3+Bt^2+Ct+D$$

anonymous · Answer

Okay it's just strange because our professor only gave us a few set things that g(t) can be, g(t) being 36t^3.  I'll try it and let you know what I get.

freckles · Answer

http://tutorial.math.lamar.edu/Classes/DE/UndeterminedCoefficients.aspx there is a table on this site that might help you in the future for determining possible particular solutions

freckles · Answer

there is a couple of lines after the table I find important too when it comes to mixing

anonymous · Answer

Yeah, I saw that page.  Our professor basically gave us a replica of that table to use but it didn't seem like it contributed to this problem.

freckles · Answer

well that last column says if g(t) is a polynomial of nth degree then your particular solution guess will be a polynomial of nth degree

freckles · Answer

here your g(t) is 36t^3 which is a cubic
so your particular solution guess will be a cubic (the one I wrote above)

anonymous · Answer

Okay, that makes sense.  Thank you!

freckles · Answer

yeah the g(t) thing is just referring to this setup:
$$y''+p(t)y'+q(t)y=g(t)$$

freckles · Answer

but anyways if you need more help on this problem let me know

anonymous · Answer

Will do, I appreciate it.