Question

Consider the following initial value problem to be solved by undetermined coefficients. Y" – 16y = 8, 7(0) = 1, y'(O) = 0 Write the given differential equation in the form L(y) = g(x) where L is a linear operator with constant coefficients. If possible, factor L. (Use D for the differential operator.) y = 8 Find a linear differential operator that annihilates the function g(x) = 8. (Use D for the differential operator.) Solve the given initial-value problem. Y(X) = Need Help? Read It Talk to a Tutor

Answer 1

y"-lby a 8 loliy loan (a) y''-lbyr 8 (0²16) y = 8 ((0-4) (044) ya 8 Llys gin ginia 8 and L=[(D-4) (D44)] o linear Differential operater that annihility ginie 8 So ; Use Degenn] = 0[8] 3 018) - 5 (8150 So, 0 =8

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