Input-output relations: Consider a linear equation
u′+c(t)u=d(t).
In many engineering and experimental sciences, the function d is called an “input” and the solution u is termed as an “output” corresponding to the input d. In the following cases, determine the output u, which is zero at t=0:
(a) u′+3u=5;
(b) u′+2u=e−t ;
(c) u′+2u=f(t), where f(t)={1, for t<0,2, for t≥0.
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