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y′′(t) +ty′(t)−2y(t) = 2, y(0) = 0,y′(0) = 0 . This is a non-homogeneous linear second-order...

y′′(t) +ty′(t)−2y(t) = 2, y(0) = 0,y′(0) = 0 . This is a non-homogeneous linear second-order differential equation withnon-constantcoefficients andnotof Euler type.

(a) Write the Laplace transform of the Initial Value Problem above.

(b) Find a closed formula for the Laplace transformL(y(t)).

(c) Find the unique solutiony(t) to the Initial Value Problem

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