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Consider the initial value problem y′′−9y′+20y=0       y(0)=2, y′(0)=4. a. Take the Laplace transform of both sides of the...

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Basic Math

Consider the initial value problem

y′′−9y′+20y=0      y(0)=2, y′(0)=4.

a. Take the Laplace transform of both sides of the givendifferential equation to create the corresponding algebraicequation. Denote the Laplace transform of y(t) byY(s). Do not move any terms from one side of theequation to the other (until you get to part (b) below).

b. Solve your equation for Y(s).

Y(s)=L[y(t)]

c. Take the inverse Laplace transform of both sides of theprevious equation to solve for y(t).

y(t)=

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