Question

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 ).

y=y=

E. Plug in the initial values and solve for c1c1 and c2c2 to find the solution to the initial value problem.

y=y=

Answer 1

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