Let c be a positive number. A differential equation of the form dy/dt = ky1+ewhere k is a positive constant, is called a doomsday equation becausethe exponent in the expression ky1+e is larger than the exponent 1fornatural growth.(a) Determine the solution that satisfies the initial condition y (0) = y0.•(b) Show that there is a finite time t=T (doomsday) such that limt→T -(t)=∞.(c) An especially prolific breed of rabbits has the growth term ky1.01 • If 2 such rabbits breed initially and the warren has 16 rabbits after three months, then when is doomsday?

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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.