1) y" - 3y' + 4y = sin 3t
Solution:
Re-arrange to get: y" = 3y - 4y + sin 3t
Let: y = x1, y' = x2, then x2' = y"
Then we can rewrite the higher order DE pair as:
x2' = 3x2 - 4x1 + sin 3t and x1' = x2 (since y = x1 and y' = x2))
2) 2 d2y/ dt2 + 4 dy/dt – 5y = 0
Divide through by 2 and transpose terms to get:
d2y/ dt2 = - 2 dy/dt + 5y/ 2
Let: y = x1, dy/dt = y' = x2, so that: d2y/ dt2 = x2'
Then:
x2' = -2 x2 + 5 x1/2, and x1' = x2
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