I need help with a math problem

Emma333 · 2018-03-20 19:05:36

Hi, I have an exam tomorrow but I do not really understand a question in my example exam. So if someone here could help me with it that would be cool.

Given is the differential equation Y" + aY' + bY = f(t)
The general solution is the sum of the homogeneous solution and the particular solution.
Given is Y" - 5Y' + 6Y = 6tˆ2 - 4t with Y(0)=5 and Y'(0)=4
Give the exact solution for Y(2)

I know the answer of the question, but there's no good explanation on how to get the answer. The given answer is:

y(t) =tˆ2 + t + 1/2 is the particular solution
Y(t)= Aeˆ2t + Beˆ3t + tˆ2 + t + 1/2 is the regular solution
Y(t) = 10.5eˆ2t - 6eˆ3t + tˆ2 + t + 1/2
Y(2) = 10.5eˆ4 - 6eˆ6 + 6.5

Getting the particular and regular solution is the part I don't understand, ofcourse the last two steps are not hard, and I understand those.
I know how to solve an equation that looks like Y"+aY+bY=0, but nowhere in my book can I find a question like this. So getting some help would be great

edit: i just looked at it again and I can find the regular solution after having the particular one, it's just solving Y" - 5Y' + 6Y = 0. Now I only struggle with finding the particular one.

edit2: Okay I got it, just say the solution must look like Y(t) = at^2 + bt + c and substitute. I was thinking waay to hard on this and this topic is useless now yay.

Anatoly · 2018-03-20 20:05:46

The notation is strange.

Emma333 · 2018-03-20 20:32:40

Y" is another notation for (d^2*Y)/(d*t^2) and Y' is another notation for dy/dt if that's what you mean.

Anatoly · 2018-03-20 20:33:26

Oh so you’re talking about integrals. Can’t help here much. Just hope this exercise won’t be there.

Emma333 · 2018-03-20 20:41:32

Kind of, but now that I understand it it's pretty easy, so I hope the real exam will have a question like this

TaskManager · 2018-03-20 20:43:16

oh wow differential equations
what/where are you studying?

Emma333 · 2018-03-20 21:15:22

TaskManager wrote:

oh wow differential equations
what/where are you studying?

Final year of high school, I follow an extra math course with subjects that aren't in regular high school math. Nice part is that there's no final exam in this course, so I get to do 1 final exam less than other students in my country.

TaskManager

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#1 2018-03-20 19:05:36, last edited by Emma333 (2018-03-20 19:51:44)

I need help with a math problem

#2 2018-03-20 20:05:46

Re: I need help with a math problem

#3 2018-03-20 20:32:40

Re: I need help with a math problem

#4 2018-03-20 20:33:26

Re: I need help with a math problem

#5 2018-03-20 20:41:32

Re: I need help with a math problem

#6 2018-03-20 20:43:16

Re: I need help with a math problem

#7 2018-03-20 21:15:22

Re: I need help with a math problem

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