Consider the differential operator L(y) = y + 4y + 4y. (a) Write all the calculations...

 

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Consider the differential operator L(y) = y" + 4y + 4y. (a) Write all the calculations needed to evaluate L(y (t)), where Y(t) = e2t (b) Write all the calculations needed to evaluate L(y2(t)), where Y(t) = te-2t (c) Use your results in parts (a) and (b) to determine whether the function y(t) = 2y(t) + 7y(t) is solution of the differential equation L(y) = 0. Explain your reasoning. Consider the differential operator L(y) = y" + 4y + 4y. (a) Write all the calculations needed to evaluate L(y (t)), where Y(t) = e2t (b) Write all the calculations needed to evaluate L(y2(t)), where Y(t) = te-2t (c) Use your results in parts (a) and (b) to determine whether the function y(t) = 2y(t) + 7y(t) is solution of the differential equation L(y) = 0. Explain your reasoning.