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Consider the partially decoupled system dx (3) 6.x + 5y + 4z dt dy 3y + 2z dt (4) %3D dz (5) = 2.

Consider the partially decoupled system dx (3) 6.x + 5y + 4z dt dy 3y + 2z dt (4) %3D dz (5) = 2. dt (a) Derive the general solution. (b) Find the equilibrium points of the system. (c) Find the solution that satisfies the IC (xo, yo, zo) = (2, 5, 6).

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