the ential equation 2y" + ty'- 2y 14, y(0) = y'(0) = 0. n some instances, the Laplace transform can be used to solve linear differential equations with variable mono THEOREM 7.4.1 Derivatives of Transforms If F(s) = L{f(t)} and n = 1, 2, 3, ..., then Left)} = (-1)"_5), ds" to reduce the given differential equation to a linear first-order DE in the transformed function Y(s) = L{y(t)}. Solve the first-order DE for Y(s). Y(s) =

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Y1 Entered Y4 1 1 t t^2 e^(-2*t) t*[e^(-2*t)] (t^2) *[e^(-2*t)] (t^3)*[e^(-2*t)] At least one of the answers above is NOT correct. [e^(1*t)]*cos(1*t) e(-21) [e^(1*t)]*sin(1*t) 37 = 3(-21) 3/2 t Y3 2 Y5 te Ys -21 Answer Preview Y6 1²e (-21) el cos(lt) (You can enter your answers in any order.) 1 Y9 t t² -21 -21 te t²e-2t A 9th order, linear, homogeneous, constant coefficient differential equation has a characteristic equation which factors as follows. t³e-2t (²6r+18)r³(r − 3)¹ = 0 Write the nine fundamental solutions to the differential equation as functions of the variable t. elt cos(lt) e¹t sin(lt) Result correct e¹f sin (lt) correct correct incorrect incorrect incorrect incorrect incorrect incorrect

Attached below is a description and the differential equations problem/question: What is the inverse Laplace transform of the given equation: W(x) = (2e^(-x)) / (x2*(x+2)) ?