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Consider the inhomogeneous differential equation

du/dt = au + b,

where a, b are constants.

(a) Show that u* = - b/a is a constant equilibrium solution.

(b) Solve the differential equation.

(c) Discuss the stability of the equilibrium solution u*.

du/dt = au + b,

where a, b are constants.

(a) Show that u* = - b/a is a constant equilibrium solution.

(b) Solve the differential equation.

(c) Discuss the stability of the equilibrium solution u*.