In this problem you will use undetermined coefficients to solvethe nonhomogeneous equation
y???6y?+9y=12te3t?6e3t+18t?21y??6y?+9y=12te3t?6e3t+18t?21
with initial valuesy(0)=?3andy?(0)=?2.y(0)=?3andy?(0)=?2.
A. Write the characteristic equation for theassociated homogeneous equation. (Use r for your variable.)
B. Write the fundamental solutions for theassociated homogeneous equation.
C. Write the form of the particular solutionand its derivatives. (Use A, B, C, etc. for undeterminedcoefficients.
D. Write the general solution. (Use c1 and c2for c1c1 and c2c2 ).
E. Plug in the initial values and solve forc1c1 and c2c2 to find the solution to the initialvalue problem.
