3. Consider4 the homogenous linear second order differential
equation
y′′ − 2y′ + y = 0 (⋆)
(a) Verify that the function y = e^x is a solution of equation
(⋆) on the interval (−∞, ∞).
(b) Verify that the function y = xex is a solution of equation
(⋆) on the interval (−∞, ∞).
(c) Verify that y = 7e^x + (5xe)^x is a solution of equation
(⋆) on the interval (−∞, ∞).
(d) Assume that c and d...