Heaviside Step Function

• May 15th 2013, 12:39 AM
weebleofthewise
Heaviside Step Function
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.
• May 15th 2013, 01:43 AM
zzephod
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\$.