5. Solve the following simultaneous differential equations: dx dy (i) + 5x + y = et, x + 3y = e²t, dt dt dx dy dx dy (ii) + 2y = 2 cost - 7 sint, + + 2x = 4 cost - 3 sint, dt dt dt dt dx dy (iii) + 2x + 5y = et. dt dt + 4x + 3y = t, -

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Q: 1. 2x + 4y + 3: = 15 4x + 5y + 3: == 24 6r + 5y + 5z = 22

A: 1. 2x + 4y + 3z = 15    4x + 5y + 3z = 24    6x + 5y + 5z = 22    243453655 xyz = 152422Augmented…