Question: (a) Solve the ODE y' - y/x = -x -1 cos (1/x). Find an initial condition for which the arbitrary constant becomes zero. Graph the

(a) Solve the ODE y' - y/x = -x^-1cos (1/x). Find an initial condition for which the arbitrary constant becomes zero. Graph the resulting particular solution, experimenting to obtain a good figure near x = 0.

(b) Generalizing (a) from n = 1 to arbitrary n, solve the ODE y' - ny/x = -x^n-2 cos (1/x). Find an initial condition as in (a) and experiment with the graph.

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