Question

solve the following initial value problem:
t(dy/dt)+5y=3t with y(1)=3

Answer 1

Same thing as before.

What is the integrating factor for this equation? How do you find it?

Answer 2

thats the question i have on web work

Answer 3

The method is all here, and worth the time to learn:
http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/lecture-3-solving-first-order-linear-odes/

Answer 4

thanks

Answer 5

im doing the same why which i got y=((3/7)t^7+(18/7))/t^5 but its wrong i dont know why can u help

Answer 6

So what is this equation in standard form and what is its integrating factor?

Answer 7

i got it the video helped me alot but i have another problem and i stock with integrate of -9t*e^-t dt can u help plz

Answer 8

Following exactly the procedure of the lecture, what is the equation in standard form; i.e., the coefficient of y' is 1.

It is

y' + (5/t)y = 3

Now, what is the integrating factor?

Answer 9

no is not the same coz my right side is -3t so when im mult by e^-t then i dont know how to integrate it ???

Answer 10

I don't know where you're getting this e^(-t) business. That has got absolutely nothing to do with the solution or the method of solution.

Answer 11

Is or is not your IVP this:
t(dy/dt)+5y=3t with y(1)=3

Answer 12

no is from different question whis is (dy/dt)-y=-9t

Answer 13

Oh, your first problem.

Answer 14

Ok. Yes, the integrating factor here is e^(-t)

Answer 15

ok then ill mult by both side

Answer 16

i got -9t*e^-t

Answer 17

for right side

Answer 18

so

e^(-t).y' - e^(-t).y = -9t.e^(-t)

i.e., [ e^(-t).y ]' = -9t.e^(-t)

Now you need to integrate both sides w.r.t. t

\[e^{-t}y(t) = \int\limits -9te^{-t} \ dt\]

So next step is evaluating this integral.

Answer 19

ok

Answer 20

so how to integrate the right side ?

Answer 21

This is why you spent a lot of time in the calculus course before your ODE course practicing integrals.

For this one, use integration by parts.

Answer 22

can u show me how coz i dont remember it

Answer 23

Post a new question with that integral. That kind of integration question is something a lot of people on here can help you with. I haven't time right now.

Answer 24

ok thanks