Question

Find the unique solution to the differential equation

yʹʹ−11yʹ+30y=−60t^(2)+104t−56

satisfying the initial conditions y(0)=6 and yʹ(0)=41
Answer: y(t)=
Your answer should be a function of t.

Answer 1

I mostly don't understand how to get the right hand side of the equation. So far I've only done these when the right side was 0

Answer 2

don't you choose y=at^2+bt+c and don't forget to add your homogenous solutions

Answer 3

c1 e^(5 t)+c2 e^(6 t)-2 t^2+2 t-1
Does that seem right?

Answer 4

so far i got a=-2 let be check your b and c

Answer 5

i got a different coefficient for t

Answer 6

i got 21/5

Answer 7

so you got c1 e^(5 t)+c2 e^(6 t)-2 t^2+(21/5)t-1 ?

Answer 8

I got y[t] = -1 + 3 E^(5 t) + 4 E^(6 t) + 2 t - 2 t^2

Answer 9

Yeah I got that too, I'll see if it's right

Answer 10

It is, I've checked with a DSolve software.

Answer 11

Okay great thanks a lot

Answer 12

no problem!

Answer 13

I'm new to this, do I press something to rate you or something?

Answer 14

I'm not sure, I'm new too. probably clicking become a fan does the trick.