# Method of undetermined coefficients for the input functions associated with the unit step

I am trying to solve a second order non-homogeneous differential equation where $x(t)$ has $u(t)$, the unit step as a part. i.e. $x(t)= f(t)u(t)$

I know how to 'guess' the particular solution for $f(t)$ alone, but I'm not sure how it should be done when the unit step is appended.

Is there a standard method for guessing the particular solution in this scenario?

E.g.

$$\frac{\mathrm{d}^2 y}{\mathrm{d} t^2} + 2\frac{\mathrm{d} y}{\mathrm{d} t}+2y = \sin(3t)u(t)$$

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and $u(t)$ is the unit step at what value of $t$? (I assume it steps up at $t=0$, but I'm just making sure...) – apnorton May 21 '13 at 17:30
yes, it's the standard step. u(t)=1 for all t>=0 and otherwise u(t)=0 – Tharindu Rusira May 21 '13 at 18:41
Wait a second... did you mean to mix the variables $x$ and $t$ in your example? (I think I misunderstood your question to start off with... ;)) – apnorton May 21 '13 at 19:13
Oh I'm sorry @anorton, it was a mistake. Both x and y are functions of t. – Tharindu Rusira May 22 '13 at 3:57