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Problem regarding the differential equation

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Problem: In a chemical reaction, a compound X is formed two compounds Y and Z. The masses in grams of X, Y and Z present at time t seconds after the start of the reaction are x, 10 - x and 20 - x respectively. At any time the rate of formation of X is proportional to the product of the masses of Y and Z present at the time. When t = 0, x =0 and dx/dy = 2.

(i) Show that x and t satisfy the differential equation

Dx/dt = 0.01(10 - x)(20- x)

(ii) Solve this differential equation an obtain an expression for x in terms of t.

(iii) State what happens to the value of x when t becomes large.

Reference no: EM13838493

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