Question

d2y/dt2+5*dy/dt+3=2u(t)where u(t) is the single input funtion of time y(0)=dy/dt(0)=0. what are the functions of the time in the solution to the ODE for output y(t) for each of the following cases u(t)=be^-2t

Answer 1

Meant to link to this one: well worth the 50 minutes to understand the theory.
http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/lecture-13-finding-particular-sto-inhomogeneous-odes/

Answer 2

And I
meant to link this one for non-homogeneouse second-order ODE's
http://tutorial.math.lamar.edu/Classes/DE/NonhomogeneousDE.aspx

Answer 3

could you work it for me or show how I should start

Answer 4

Also remember that this equal has two homogeneous solutions and then you need to find the particular solution

I assume you meant to write that the homogeneous equation is
y'' + 5y' + 3y = 0
So substitute a trial solution/Ansatz of y = e^(ax)
and solve for a

That gives you two homogeneous solutions.

Answer 5

the two main methods I know of are variation of parameters and undetermined coefficients. I think undetermined coefficients works better her. Like James said start with the complimentary solution,
and try this stuff http://tutorial.math.lamar.edu/Classes/DE/UndeterminedCoefficients.aspx

Answer 6

ok i will try that method
thanks

Answer 7

so would I get a particular answer and a complimentary answer ?

Answer 8

I posted lecture 13. Based on your question, you should also watch lecture 11.