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For added spice, you may not use your calculator here. b, Show that [tex: \frac { d } { dx } ( \frac { 1 } { 2 } ln(cotg x)) = -cosec 2x ] c, Show that [tex: \sqrt (cotg x) ] is an integrating factor for this ODE d, Solve the ODE for y e, Consider the results from (d) and (a), and that (d) is valid for [tex: 0 < x < \frac { \pi } { 2 } ] .