Mathematics, 27.11.2019 05:31 garzamatt7

Let c be a positive number. a differential equation of the form

dy
dt= ky1 + c
where k is a positive constant, is called a doomsday equation because the exponent in the expression ky1 + c is larger than the exponent 1 for natural growth.

(a) determine the solution that satisfies the initial condition

y(0) = y0.

ans: y=(-ckt+y0^-c)^(-1/c)

(b) show that there is a finite time
t = t
(doomsday) such that
lim t %u2192 t%u2212y(t) = infinity.
ans: y(t) --> infinity as 1-cy0^ckt--> 0 as t--> 1/cy0^ck
t=1/cy0^ck, them lim y(t)=infinity as t--> t-

Answers: 3

Show answers

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 14:30, kadrian12

Graph the system: f(x)= 3/x-2; f(x)= 1/2x + 2

Answers: 3

continue

Mathematics, 21.06.2019 14:50, amcdaniel1

Which function has the same domain as y=2x

Answers: 1

continue

Mathematics, 21.06.2019 17:00, gomez36495983

() at a farm, animals are fed bales of hay and buckets of gain. each bale of hay is in the shape of a rectangular prism. the base side lengths 2 feet and 3 feet, and the height is 5 feet. each bucket of grain is a cylinder with diameter of 3 feet. the height of the bucket is 5 feet as the height of bale. a. which is larger in area, the rectangular base of the bale or the circular base of the bucket? explain how you know b. which is larger in volume, the bale or the bucket? explain how you know

Answers: 1

continue

Mathematics, 21.06.2019 22:30, alvaradorosana05

Shannon drove for 540 minutes. if she traveled 65 miles per hour, how many total miles did she travel?

Answers: 2

continue

You know the right answer?

Let c be a positive number. a differential equation of the form

dy
dt= ky1 + c