In this problem you will use undetermined coefficients to solve the nonhomogeneous equation y"−6y′+9y=18t−39−(18te3t+6e3t)y″−6y ′+9y=18t−39−(18te3t+6e3t)
with initial values y(0)=−1andy′(0)=11.
A. Write the characteristic equation for the associated homogeneous equation. (Use r for your variable.)
B. Write the fundamental solutions for the associated homogeneous equation.
y1= y2=
C. Write the form of the particular solution and its derivatives. (Use A, B, C, etc. for undetermined coefficients.
Y=
Y′=
Y″=
D. Write the general solution. (Use c1 and c2 for c1c1 and c2c2).
y=
E. Plug in the initial values and solve for c1c1 and c2c2 to find the solution to the initial value problem.
y=

Ican interpret and represent the remainder in division calculations sensibly for the context (eg if we wont to know how many 40 seat buses will be needed to transport 170 students for on excursion, we divide 170 by 40 and realise buses and another smaller vehicle to that we need 4 transport 10 more students) solve the following questions. show your work! 11) the zoo had 420 butterflies that needed to be transported to a new enclosure. the boxes that the butterflies would be moved in only hold 80 butterflies in each. how many boxes would they need? 2 12) each classroom in the school can have exactly 25 students, if there are 345 students in the school how many full classrooms are there?