QUESTION 1 a) Show that the given differential equation is exact. Hence, obtain the general solution....

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QUESTION 1 a) Show that the given differential equation is exact. Hence, obtain the general solution. (yey + )dr + (xe-)dy = 0. b) Use the substitution to solve the differential equation sin y dy tan y = dr 'sin y cos y c) A mass m which falls through the air towards earth with velocity v can be modelled by the differential equation dv = mg – bv, dt m- where m, g and b are constants. (i) Find its velocity at any time t if m = 20 kg, g = 9.8 ms-2 and b = 2 kgs-. (ii) Find the limiting velocity ast approaches infinity. QUESTION 1 a) Show that the given differential equation is exact. Hence, obtain the general solution. (yey + )dr + (xe-)dy = 0. b) Use the substitution to solve the differential equation sin y dy tan y = dr 'sin y cos y c) A mass m which falls through the air towards earth with velocity v can be modelled by the differential equation dv = mg – bv, dt m- where m, g and b are constants. (i) Find its velocity at any time t if m = 20 kg, g = 9.8 ms-2 and b = 2 kgs-. (ii) Find the limiting velocity ast approaches infinity.