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Find the general solution for each of the given systems and draw a phase portrait. Describe the behavior of the solutions as t rightarrow infinity and as t rightarrow infinity. x' = x x' = x x' = x. Find the Laplace transform of the following functions by using a a table and/or basic properties. You do not need to compute any integrals. f(t) = -2 f(t) = e-2t f(t) = sin 3t f(t) = te-3t f(t) = e2t cos 2t Sketch each of the following piecewise functions and compute their Laplace transforms. f(t) = f(t) =

Show transcribed image text Find the general solution for each of the given systems and draw a phase portrait. Describe the behavior of the solutions as t rightarrow infinity and as t rightarrow infinity. x' = x x' = x x' = x. Find the Laplace transform of the following functions by using a a table and/or basic properties. You do not need to compute any integrals. f(t) = -2 f(t) = e-2t f(t) = sin 3t f(t) = te-3t f(t) = e2t cos 2t Sketch each of the following piecewise functions and compute their Laplace transforms. f(t) = f(t) =