Use direct substitution to verify that y(t) is a solution of the
given differential equation in Exercise Group 1.1.9.15–20. Then use
the initial conditions to determine the constants C or c1 and
c2.
17. y′′+4y=0, y(0)=1, y′(0)=0, y(t)=c1cos2t+c2sin2t
18. y′′−5y′+4y=0, y(0)=1 , y′(0)=0,
y(t)=c1et+c2e4t
19. y′′+4y′+13y=0, y(0)=1, y′(0)=0,
y(t)=c1e−2tcos3t+c2e−3tsin3t
27. The growth of a population of rabbits with unlimited
resources and space can be modeled by the exponential growth
equation, dP/dt=kP.
Write a differential equation to model a population of...