In this problem you will use undetermined coefficients to solve
the nonhomogeneous equation
y′′−6y′+9y=12te3t−6e3t+18t−21y″−6y′+9y=12te3t−6e3t+18t−21
with initial values
y(0)=−3andy′(0)=−2.y(0)=−3andy′(0)=−2.
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=y1=
y2=y2=
C. Write the form of the particular solution
and its derivatives. (Use A, B, C, etc. for undetermined
coefficients.
Y=Y=
Y′=Y′=
Y′′=Y″=
D. Write the general solution. (Use c1 and c2
for c1c1 and c2c2...
Consider the following differential equation to be solved by the
method of undetermined coefficients.
y'' + 6y =
−294x2e6x
Find the complementary function for the differential
equation.
yc(x)
=
Find the particular solution for the differential equation.
yp(x)
=
Find the general solution for the differential equation.
y(x) =