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Solve the given initial-value problem in which the input function g(x) is discontinuous. [Hint: Solve the...

Solve the given initial-value problem in which the input function g(x) is discontinuous. [Hint: Solve the problem on two intervals, and then find a solution so that y and y' are continuous at

x = π/2.]

y'' + 4y = g(x),   y(0) = 1, y'(0) = 3,   where

g(x) =

sin(x),    0 ≤ x ≤ π/2
0,    x > π/2

Find y(x) for each of the intervals.

  ,    0 ≤ x ≤ π/2
  ,    x > π/2
Math   Advanced-Math   
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