a) A large field of area 4km^2 is becoming infected with a soil disease. At time t years the area infected is xkm^2 and the rate of growth of the infected area is given by the differential equation dx/dt = kx(4 — x), where k is a positive constant. It is given that when t = 0, x = 0.4 and that when t = 2, x = 2. (i) Solve the differential equation and show that k = 0.25ln(3) (ii) Find the value of t when 90% of the area of the field is infected.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.