Consider the dierential equation y'' + 4y' + 29y = 7t^3e^(-2t) cos(5t) : The reasoning behind your answers should be made clear. A.1. The forcing has a characteristic form. Give its degree, characteristic, and multiplicity. A.2. Write down the Key Identity and its derivatives with respect to z up to the order needed for the Key Identity Evaluation method. (You do not need to evaluate these at the characteristic.) A.3. Write down the form for the particular solution needed to start the Undetermined Coefficients method. (You do not need to plug this form into the differential equation.)
Consider the dierential equation
y'' + 4y' + 29y = 7t^3e^(-2t) cos(5t) : The reasoning behind your answers should be made clear.
A.1. The forcing has a characteristic form. Give its degree, characteristic, and multiplicity.
A.2. Write down the Key Identity and its derivatives with respect to z up to the order
needed for the Key Identity Evaluation method. (You do not need to evaluate these at the characteristic.)
A.3. Write down the form for the particular solution needed to start the Undetermined Coefficients method. (You do not need to plug this form into the differential equation.)
A.4. Use the Green Function method with initial time 0 to express a particular solution in terms of two denite integrals that do not have t in their integrands. (You do not need to evaluate these integrals.)
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