d²s ds +6-+ 4.5s = 0 dt

Q: A mining expert estimates that the production growth rate of copper overtime, or is given by dt' dy…

A:

Q: The equation = xy? +2y +x-4.5 with the initial condition y(x = 0) = 1 is to be solved dx %3D using a…

A:

Q: A new type of bacteria is found in a sample of food. Suppose P(t) denotes the population size of the…

A:

Q: the above equation numerically, you need to approximate the second and first orde d21 dl and dt'…

A: Given:   Ld2 Id t2+RdIdt+1c I =E(t) L= 1H R =10Ω c=0.0025 F E(t)=-0.08 cos 2.5t and ∆t=0.01 s The…

Q: The approximate value of y(3) for the initial value problem for ' = cost + sint, y (0)=0.5 with h=…

A: Correct option is (b) 2.631 Detailed solution : Given y′=cos(t)+sin(t),y(0)=0.5,h=0.5,y(3)=?Forth…

Q: Please answers part c, d

A: As per norms, the first three questions are answered. The questions concern the linear approximation…

Q: The number of fish, P, in a lake with an initial population of 10,00 dP = kP – r. dt satisfies, for…

A: To determine the value of r so that the population of fish remains constant.

Q: The finance department of a car company conducted a study of their weekly sales in the past years,…

A: Given, st=12.18cos0.88t-7.25+20.40,  t≥0 a weekly sales at the start of study find sales at t=0…

Q: The Verhulst (or logistic) DE can be adapted to include "harvesting" to model a fishery population,…

A:

Q: A mining expert estimates that the production growth rate of copper overtime, or ,is given by dt' dy…

A: By using integration.

Q: A materials scientist is experimenting with a new material with which to make beverage cans. She…

A: From the given plots, the scatterplot shows a perfect negative relationship between the variables.…

Q: dy = te2t – y, 0 < t < 1, y (0) = 1, with h = 0.5; dt -

A: The formula for iteration using the Euler method i: Here, h is the step size and f is the function…

Q: Find the temperature u(x,t) from the heat equation in a laterally insulated copper bar 80cm cm long…

A:

Q: With what initial velocity v0 must we fire a rocket so it attains a maximum height r above the…

A: We will use the maximum height formula Where u=initial velocity. g=gravity H_max= maximum height

Q: Q4. (a) Use the method of integrating factor, solve the following dy + 2y = pe-2t – qe³t dt with the…

A:

Q: A particle moves along the x-axis so that at time t 0 its velocity is given by v(t) = 3t2 - 6t 24.…

A:

Q: You bail out of a heicoptor and immediately pull the ripcord of your parachute. Your downward…

A:

Q: The speed of the motor, w of a centrifuge in a Chemical Engineering Laboratory is given by equation…

A: Differential equation is a equation that represents the relation between variable and their…

Q: The velocity of a falling object satisfies the following initial value problem dv = 9.8 – v, v(0) =…

A:

Q: A mining expert estimates that the production growth rate of copper overtime, or "/dt, is given by…

A:

Q: The concentration of pollutant bacteria e in a lake decreases according to c = 70 e 1.5t + 25…

A: Given c = 9, then 9 = 70e-1.5t+25e-0.075t, we can rewrite it as f(t) = 70e-1.5t+25e-0.075t-9

Q: A 2-lb object, that stretches a spring by 1.5 inches, is released with a downward velocity of 32…

A:

Q: A particle moves in a straight line with a velocity of v' (t) = /3t –1 meters per second, where t is…

A: Simpson 38 rule…

Q: 4. A certain particle is travelling in a straight line governed by the equation a = v5 m / s?. If…

A: we know the first equation of motionv=u+atv=1+2v95  m/s

Q: A cat falls from a tree (with zero initial velocity) at time t = 0. How far does the cat fall…

A:

Q: The barometric pressure p (in inches of mercury) at an altitude x miles above sea level satisfies…

A:

Q: Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), x(a)…

A: As this problem is related to vector differential equation of a matrix, hope you know how to find…

Q: A particle moves along the x-axis so that at time t\ge 0t≥0 its position is given by…

A:

Q: 3. The formula g = 2s /is used to determine the acceleration of gravity. For a possible error of 1%…

A: Let's find.

Q: The acceleration function (in m/s²) and the initial velocity are given for a particle moving along a…

A: Given

Q: Solve the initial value problem for y as a function of x. dy x² + 121) 3 23, у(11)%3D0 dx The…

A: Topic:- integration

Q: A rocket, fired from rest at time t = 0, has an initial mass of m0 (including its fuel). Assuming…

A: Given m(t)=m0-kt and the differential equation as…

Q: The displacement of a structure is defined by the following equation for a damped oscillation y =…

A: By this method 1st we will find an interval where roots can lie and then use xn+1=xn-f'(xn)f(xn) to…

Q: You bail out of a helicopter and immediately pull the ripcord of your parachute. Your downward…

A: Given the differential equation dvdt=32-1.6v,v0=0. Euler's method is given by vn+1=vn+hftn,vn. In…

Q: (c) f(t) = e e-2t cost MUCS Yp(t) (d) f(t) = (3t² +t) cos t MUCS Yp(t) :

A:

Q: For the equation y 00 + by0 + 3y = f(t), where y 0 = dy/dt. (a) Find the range of values of b for…

A:

Q: A particle moves along the x-axis so that at time t> 0 its position is given by x(t) = -t3 +11t?…

A: For the given position vector  x(t) = -t3+11t2-24t Velocity at t = 7 is calculated as shown below

Q: The period T of a simple pendulum is given by T=2π√L/g where L is the length of the pendulum and g…

A:

Q: A particle moves along the x-axis so that at time t > 0 its velocity is given by v(t) = 3t² – 30t –…

A: topic - quadratic equations

Q: A rocket, fired from rest at time t=0, has an initial mass of m0 (including its fuel). Assuming that…

A: Let m(t) and v(t) be the mass and velocity of the rocket at time t. If m0 is the initial mass at…

Q: A rocket accelerates by burning its onboard fuel, so its mass decreases with time. Suppose the…

A: you can clearly understand if you follow the below solution

Q: According to one model that attempts to account for air resistance, the distance s(t)(in meters)…

A:

Q: A spring of constant k=8 N/m hanging from the ceiling is placed at its lower end with an object of…

A:

Q: A body is dropped (initial velocity being 0) from a distance ro from the earth's center. Ignoring…

A: The acceleration is given by . We can rewrite  using the chain rule as . Replace  in . Integrate…

Q: Solve the initial value problem y" + 2y' +y = et+ 8(t – 3); y(0) = 0, y' (0) = 3. %3D - Justify your…

A:

Q: 1. A particle moves along the x-axis according to the equation x=2r+3F, where x is in m and is in…

A:

Q: The velocity is equal to the rate of change of distance x (m), dx v(t) dt (1.1) a. Substitute Eq.…

A: After substituting Eq. (1.2) to Eq. (1.1), we have dxdt=gmc1−e−cmt

Q: Imagine that a block of mass 1 kg is attached to a ceiling by a spring with constant 5 kg/s? and a…

A:

Q: A cylindrical tank of height 13 metres is full of water at time t = 0 seconds. is turned on at the…

A:

Q: A particle moves along the x-axis so that at time t 0 its position is given by a(t) = -t + 4ť² – 4t.…

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.