# Homework Help: Urgent: Needed for Calculus Exam!

1. Oct 31, 2004

### Hyperreality

Just a question to clear things up regarding to the integrating factors for my exams tomorrow:

The standard first order differential equation has the form:

dy/dx + p(x)*y = q(x).

where the integrating factor is e^(integral of p(x) dx).

But in one of the previous year paper, it has the equation

dy/dt + bt = a

where "b" and "a" are constants. To me, this does not resembles the standard form.

But apparently it is, in the answer they used the integral factor
e^(integral of b) and solved the equation.

I must have missed some important points in how to identify integrating factors...

2. Oct 31, 2004

### cepheid

Staff Emeritus
It's a special case of the standard from in which p(x) and q(x) are constant functions! So, it's an easier to solve case. But it's still a linear equation, so why wouldn't the method of integrating factors work? The standard form is just the most general case.

Edit: Why did you post a question about differential equations in the Kindergarten to Grade 12 HW Help forum? :rofl:

Edit: I didn't read the problem carefully before. Furthermore, it should be even easiser to solve, because p(x) = 0! There is no 'y' term.

Edit: At third glance, the problem is SO easy, that although it is a linear equation, it doesn't even merit the method of integrating factors! You have dy/dt = q(t). Why not just integrate directly?

$$\frac{dy}{dt} = a - bt$$

$$y = \int{(a-bt)}dt$$

Right?

Last edited: Oct 31, 2004