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=