Re: Heaviside Step Function

Quote:

Originally Posted by

**weebleofthewise** Hello, I hope someone can help me with my Ordinary Differential Equations homework. The chapter is on Heaviside Step Function.

The problem says: In each case evaluate x'(2), x'(5), and x''(5).

One similar to the one I have to work is: t^2+H(t-3)*exp(-2*t)

The books gives the following answers:

x'(1.3) = 2.6

x'(4) = 8 - 2*exp(-8)

x''(4) = 2 + 4*exp(-8)

I'm not sure what I'm suppose to be doing, thanks for your help.

If $\displaystyle t<3$ then $\displaystyle x^{(n)}$ is the $\displaystyle n$-th derivative of $\displaystyle t^2$, if $\displaystyle t>3$ it is the $\displaystyle n$-th derivative of $\displaystyle t^2+\exp(-2t)$ and there are no derivatives at $\displaystyle t=3$.