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The temperature \(x\) of a drink \(t\) seconds after ice cubes are added to it, satisfies the differential equation$$ 50\dfrac{d^2x}{dt^2} + \dfrac{dx}{dt} = 0 $$
  1. Use the substitution \(y = \dfrac{dx}{dt}\) to write this as a coupled system of first order differential equations.
  2. The equation for \(\dfrac{dy}{dt}\) is separable and independent of \(x\). Solve this equation for \(y(t)\).
  3. Hence find a general solution for \(x(t)\).

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