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 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.

Transcribed Image Text:

dx dt = kx2,