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Find the Laplace transform of a) e^(2t)sin(3t) and the inverse Laplace transform of b) e^(-s)/(s^2 + 2s + 5).
Show that the set of rational functionsp(x)/q(x),q(x) can't be 0, forms a field. Herep(x), q(x) are polynomialswith rational cofficients.
Solve using any technique y'' - 2y' - 3y = 3e^(3x),y(0) = 3, y'(0) = 7/4
Find the equation of the line that contains the given points.P1(0, 2), P2(3, 5)
Find the dimensions of the largest rectangular box in the first octant of the xyz-coordinate system that has one vertex at the origin and the opposite vertex on the plane x + 2y + 3z = 6.