Order of a Differential Equation

[debrox]

Hi. I'm reading a differential equation book to prime myself best for my signals and systems class I'm in, and I've ran into some confusion.

If I had a differential equation like so:

$$y'(t) + \int y(t)dt = f(t)$$ (1)

What would you say the order is? The definition says "the order of a differential equation is the highest derivative that appears in the equation."

Would I say it's a second order differential equation because:

$$h(t) = \int y(t)dt$$ (2)
meaning:
$$h''(t) = y'(t)$$ (3)
and substituting (2) and (3) into (1):
$$h''(t) + h(t) = f(t)$$ (4)

If asked to solve such a differential equation, would I first solve (4) and then differentiate h(t) to find y(t), the original function of t in question?

 

[HallsofIvy]

What you have initially is NOT a "differential equation". It is an "integra-differential equation" and the term "order" does not apply to it. Assuming f(t) is some reasonable function, then yes, the method you describe for solving it should work.