15.8 SOLUTION OF DIFFERENTIAL EQUATIONS BY LAPLACE TRANSFORMS
One of the important applications of Laplace transform is in solving linear constant-coefficient ordinary differential equations with initial conditions. The procedure is illustrated below through an example.
EXAMPLE: 15.8-1
Find y(t) for t > 0+ for x(t) = 2tu(t) in the given differential equation with y(0–) = 1, y'(0–) = –1 and y” (0–) = 0.
SOLUTION
A differential equation is an equation in which both sides of it can be multiplied by e–st. Since the differential equation is satisfied at all instants of time, both sides of it can be integrated with respect to time from 0–
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