# 1. (a) Write down a second-order differential equation such that y(x) = 3xe-20 is a solution....

###### Question:

1. (a) Write down a second-order differential equation such that y(x) = 3xe-20 is a solution. (b) Determine whether the pair of functions y1 (2) = x sin(x) and y2(x) = cos(x) are linearly inde- pendent. Justify your answer. (c) Write down a second-order ODE which has a solution y(x) that is bounded for all 3 (i.e. y(x) < for all 2) but y(x) is not a constant function.

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