Question

Find the function satisfying the differential equation
f'(t)-f(t)=-9t and the condition f(1)=9

Answer 1

What is the integrating factor?

Answer 2

In other words, we're looking for a function u(t) such that

(uf)' = uf' + u'f = u(f' - f) ------- (*)

Once we have that function we will be able to multiply your equation by u and hence

(uf)' = -9t.u(t)

and now just integrate.

So. What is u? This is the integrating factor.

I.e., what is the integrating factor for your equation?

Answer 3

If you're completely lost by whatI just wrote, I recommend you either go back to your text book or watch this good lecture:

http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/lecture-3-solving-first-order-linear-odes/

Answer 4

f is factor of (t)

Answer 5

coz i need to find f(t) = ?

Answer 6

f(t) is a function of t.

Answer 7

I think it's fair to say you are completely lost. Watch the lecture. He explains very well how to solve this sort of equation.