Question: Problems 43 through 46 concern the differential equation where k is a constant. (a) If k is a constant, show that a general (one-parameter) solution

Problems 43 through 46 concern the differential equation

dx dt = kx2,

where k is a constant.

(a) If k is a constant, show that a general (one-parameter) solution of the differential equation is given by x(t) = 1/(C - k t), where C is an arbitrary constant.(b) Determine by inspection a solution of the initial value problem x' = kx², x(0) = 0.

dx dt = kx2,

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