b) A population of size x is decreasing according to the law dx -x dt 250 where t denotes the time in days. If initially the population is of size x, (that is, when t = 0,x = xo) find how long it takes for the size of the population to be halved.

Q: 5. The estimated cost per sq.m. of fully furnished house construction in a given site is governed by…

A: For a differential equation of the form: y'=fx, y, Euler's method uses the formula:…

Q: dx xt x(1) = 2, solve for x(2) when h = 0.1 %| dt t²+2

A: As per the question we have to solve the following first order differential equation : dy/dx =…

Q: 2 Example 10.8. Using Euler's method, find an approximate value of y corresponding to x= 1, given…

A:

Q: A mass-spring system consists of a mass of 2 kg and the spring has a length of 0.9 m. e of 25.6…

A: In this question, concept of differential equation is applied. Differential Equation A differential…

Q: 1. If z = 2xy – 3x²y and x is increasing at 2 cm/sec determine at what rate y must be changing in…

A: Z is neither increasing nor decreasing at the given instant. A function is said to be neither…

Q: 16. Suppose the radius r, height h, and volume V of a dh related to dt dV cylinder are functions of…

A: Given: A cylinder with radius, r and height, h. The formula for the volume (V) of the cylinder is…

Q: 6) If differentiable functions y = F(x) and y = G(x) both solve the initial value problem dy f(x),…

A:

Q: A cylindrical tank initially contains 400 liters of fluid with 90 grams of salt dissolved in it.…

A: NOTE: Refresh your page if you can't see any equations. . y=amount of salt at time t

Q: This is a differential equations problem.

A:

Q: A mass weighing 4 lb stretches a spring 2 in. Suppose that the mass is given an additional 6-in…

A: mg = weight =4 lb; L = initial displacement = 2 in = 2/12 = 1/6 feet; Fdampening = Viscous…

Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given…

A: Question is solved.

Q: A clamped beam of length 3 is modeled by: y(4) = 24, y(0) = y'(0) = 0, y(3) = y'(3) = 0. Solve the…

A: The given differential equation is y4=24, with y0=y'0=0 and y3=y'3=0 Now we integrate the given…

Q: When a certain polyatomic gas undergoes adiabatic expansion, its pressure p and volume V satisfy the…

A: pv1.2=kdifferentiating both side with respect to t∂p∂tv1.2+1.2v0.2∂v∂tp=0∂p∂tv1.2=-1.2v0.2∂v∂tp

Q: 3. Sketch solution curves for a variety of initial conditions for dw = (w - 3)(w – 7). dt

A:

Q: 1. Use the Improved Euler's method to integrate dx = t - sinx dt given x(0) = 1, using a step size…

A: The given differential equation is dxdt=t-sin(x), x(0)=1, h=0.1 The formula for improved Euler…

Q: Suppose that the per capita growth rate of a population is 3%; that is, if N(t) denotes the…

A:

Q: dx 1. dt xt x(0) = 1, solve for x(0.3) when h = 0.1 I| -

A: Given function is, dxdt=-12xt,   x(0)=1, h=0.1 and we need to solve, x(0.3)   Here we have, (t0,…

Q: 5. Let f: R × R → R have many derivatives, and to,uo E R. Give the formulas, error estimates per…

A: Given that, The formula for the approximate the solution, u't=ft,ut…

Q: A cylindrical homogenous, isotropic rod with insulated sides has the temperature f(x) L/2 ={L-X…

A: Given that, A cylindrical homogenous, isotropic rod with the insulated sides has the temperature,…

Q: dx 2. dt x(0.5) = 1, solve for x(1) when h = 0.1 2(t+1)

A: It is given that, dxdt=x2(t+1),    x(0.5)=1, h=0.1 and we have to find x(1)   Here interval is 0.1,…

Q: Example 10.10. Using modified Euler's method, find an approximate value of y when x = 0.3, given…

A: We can solve this using given information

Q: Determine the largest interval in which the given initial value problem is certain to have a unique…

A:

Q: 1. The position of a particle at time t (s) is s(t) = V12 +1 m. Com- pute its average velocity over…

A: Given, The position of a particle at time t seconds is s(t)=t2+1 meter.  To find the average…

Q: 1. e-st cosh t dt 2x +4 2. 2x2 + 21x + 34

A:

Q: A 1/8-kg mass is attached to a spring with stiffness 16N/m. The damping constant for the system is…

A: In this question, we established a differential equation and solve that with given initial…

Q: A falling object satisfies the initial value problem dv 9.8- (), v(0) = 0 %3D where y is the…

A:

Q: (. ) If a mass of 7 kg stretches a spring 3 cm beyond its natural length, what is the spring…

A:

Q: Find the maximum possible temperature of an ideal gas undergoing the process p=p0e−βV, where β is a…

A: The given function is where p is the pressure ,β is a positive constant and V is the molar volume…

Q: Suppose a 50-gallon tank contains a volume V0 of clean water at time t = 0. At time t = 0, we begin…

A: (a) It is given that, a 50-gallon tank contains a volume V0 of clean water at time t = 0. At time t…

Q: 01-1. Suppose that a spherical droplet of liquid evaporates at a rate that is proportional to its…

A: Euler method is used to find the solution of an initial valued first order differential equation.…

Q: A rectangular plate with insulated surface is 10 cm. wide and so long compared to its width that it…

A: The two-dimensional heat equation is given by The steady-state heat equation without a heat source…

Q: A point is moving along the graph of the given function at the rate dx/dt. Find  dy/dt for the given…

A:

Q: 3. The parameters needed to describe the survivor curve for a microbial population at 110 °C is…

A: Given ,  D=1.2min n = 0.4 Let N be the number of survivors after a process of 10 mins

Q: 5. Suppose heat is lost from the lateral surface of a thin rod of length L into a surrounding medium…

A: Given the heat equation is k∂2u∂x2-hu=∂u∂t, 0<x<L, t>0 The initial temperature is f(x)…

Q: 9. A thin homogeneous bar of length L has initial tem- perature f(x) = Bx/L, with B a positive…

A: Let u(x,t) be the temperature of the bar. Heat equation is given by ∂u∂t=∂2u∂x2 with the initial…

Q: A 24-lb weight is attached to the lower end of a coil spring suspended from the ceiling and having a…

A: If weight of mass m is attached to a spring with spring constant k and damping constant β then by…

Q: A falling object satisfies the initial value problem dv = 9.8 – dt -(), v (0) = 0 where v is the…

A:

Q: A 1-kilogram mass is attached to a spring whose constant is 24 N/m, and the entire system is then…

A: NOTE: Refresh your page if you can't see any equations. . mass is m=1 kg the spring constant is k=24…

Q: (a) The reaction to form an iodine molecule is a second-order kinetics rate of loss of iodine atoms…

A:

Q: 2. Another equation that has been used to model population growth is the Gompertz equation dy/dt =…

A: Given Data: dy/dt =ry lnKy where r and k are positive constant (a) Find the critical points (b) To…

Q: A point is moving along the graph of the given function at the rate dx /dt. Find dy/dt for the given…

A:

Q: (a) Integrate x ln(x + 1)dx analytically; and numerically using (b) trapezoidal rule with iterations…

A: As per the rules we can solve only 3subparts per questions so I'm solving a,b,c

Q: A 16-lb weight is attached to the lower end of a coil spring sus-pended from the ceiling and having…

A:

Q: 4. A tank initially holds 80 gal of a brine solution containing 1/8 Ib of salt per gallon. At t = 0,…

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Q: A tank contains 50-liters of brine in which 20 grams of salt is dissolved. Pure water is being…

A:

Q: Suppose that a certain population satisfies the initial value problem…

A: Calculation:

Q: A certain photoelectric devise is sensitive to wavelengths up to 940 nm. a. What is the frequency…

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Q: A 1-kilogram mass is attached to a spring whose constant is 24 N/m, and the entire system is then…

A: Given m=1,k=24,β=11 The general equation of motion for a spring mass system with damping is,…

Q: solve the inhomogeneous initial value problem x = (; ) × (4 ln t X + 1 -2 X(1) = (1). %3D

A: Given,              X˙=2-41-2X+ 4lnt1t,     X(1) = 1-1                        (1)

Q: The growth of malignant tumors can be modeled using the Gompertz model. dP = r.P. In in) dt where r>…

A: (a) Let us examine the Gompertz model of malignant cell growth. Here P is the variable with respect…

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.