A model for the population P(t) in a suburb of a large city is given by the initial-value problem dp P(1 P -), P(0) = 4000, dt 1000,000 where t is measured in months. The limiting value of the population and the time will take the population be equal to one-half of this limiting value respectively are 5000, 4992 b. 1000,000, 58 C. 2500, 2498 d. 1000,000 55

Q: Solve the initial value problems in Problems and graph each solution function x(t). x" + 4x = 8(t) +…

A: Take a Laplace transform of the equation:

Q: Solve the problem: max/min U = xy subject to x2 + y2 2 %3D

A:

Q: The length l, width w, and height h of a box change with time. At a certain instant the dimentions…

A: Given that length, width and height of a box is changing and at an instant l=1 m and w=h=2 m. Also…

Q: a) A 4 kg cannonball is shot into the air with an initial upward velocity of +100 m/s. Assume the…

A:

Q: Solve the following initial value problem. у) + у'3D 9х +5е "X; у(0) %3D1, у' (0) %3 0, у'"(0) %3 1…

A: We have to find the desire solution of given differential equations.

Q: if x(t) = tsin(3t) is a particular solution to the equation x" + qx = cost3t, then q = -9. Is that…

A: The given differential equation is: x''+qx= cos t (3t) From the hypothesis, x(t)=t sin (3t) is the…

Q: Solve the following initial value problem. y" – 17y" + 63y' + 81y = 0, y(0) = 0, y'(0) = 0, y"(0) =…

A:

Q: the sho wh Solve innitial valve problem below: g/1-16y=e4x² g (0) = 10₂y '(a) = 7

A: The given equation is; y''-16y=e4x, y(0)=10, y'(0)=7

Q: ƒ(x) = ln (3-x)+²x²¹ 4

A:

Q: 8. In a permanent disability model, we have = 0.2, t = 0.1, pt = ,01 ,02 12 0.25 healthy (0)…

A: Given  μx+t01=0.2,  μx+t02=0.1,  μx+t12=0.25

Q: Given the description of the phenomena, identify the corresponding mathematical model. A population…

A: Solution

Q: Suppose that an lowa class battleship has mass around 54,000 metric tons (54,000,000 kg) and a…

A:

Q: Consider a crossbow that fires a bolt straight upward from the ground with an initial velocity of 56…

A: The given initial problem is, dvdt=f(t,v)=-0.04v-9.8, v(0)=56. To Find: (a) First 10 iterations with…

Q: Suppose that we track the velocity of Prof.Watkins' car within the first 19 seconds it is traveling…

A: The distance traveled = Area under velocity time graph = Area as per right end point aproximation

Q: I1 x₂ = x3 = || Solve the following initial value problem: 2 -10 7 +-60-~-() -1 5, z (0) 0-10 9 d dt…

A:

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.