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  3. in this problem you will use undetermined coeffici

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...

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Advance Math

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.

y1=y1=y2=y2=

C. Write the form of the particular solutionand its derivatives. (Use A, B, C, etc. for undeterminedcoefficients.

Y=Y=
Y?=Y?=
Y??=Y?=

D. Write the general solution. (Use c1 and c2for c1c1 and c2c2 ).

y=y=

E. Plug in the initial values and solve forc1c1 and c2c2 to find the solution to the initialvalue problem.

y=y=

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