Question: Question 6 (Unit 2) 12 marks (a) Determine p(z) by solving the differential equation dp 1 dz JP, = where X is a constant,

Question 6 (Unit 2) 12 marks (a) Determine p(z) by solving the

Question 6 (Unit 2) 12 marks (a) Determine p(z) by solving the differential equation dp 1 dz JP, = where X is a constant, and find the particular solution that satisfies the initial condition p(0) = P, where P is a constant. (b) A quantity o(r) satisfies the first-order differential equation 2 do dr = K, r> 0, where K is a constant. Find the particular solution of this equation that satisfies (R) = 0, where R is a constant. (c) A function P(y) satisfies the differential equation dP dy + Ay P = 0, where A is a constant. Determine the particular solution that satisfies the initial condition P(0) = 1. [4] [4] [4]

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