It is given that the metal has diffusivity a = 2.25, that the two ends of the bar are kept at temperature u = 0 and that the initial temperature distribution is u(x, 0) = f(x) = sin(rx/() %3D

Q: An insulated uniform metal rod, 40 cm long, has the temperature of its ends maintained at 0°C for…

A: In this,we cam find the expression for the temperature using given initial temperature distribution.

Q: (a) Given the initial value problem sin (x + y) + cos (xy) + dy = 0, y (0) = 0, dx approximate y…

A:

Q: The heat transfer rate of the rocket engine is given by: dT Q = -kA- dx Where k is the thermal…

A:

Q: The heat transfer rate of the rocket engine is given by: dT Q = -kA –dx Where k is the thermal…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find the function f(x) described by the given initial value problem. F'(x)=sin x , f(0)=-3

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: Find the temperature u(x, t) in a rod of length L = 2 if the initial temperature is f(x) (0 < a < 1)…

A: To find - The temperature u(x,t) in a rod whose length is L=2 and if the ends are insulated from 0…

Q: 6. · Find the temperature u(x, t) of the laterally insulated thin bar with a length when the initial…

A: Given - A laterally insulated thin bar with length π , initial temperature cos2x , boundary…

Q: Find the explicit particular solution of the initial value problem given. dy = y e X, y(0) = 2 e 5x…

A:

Q: Q1: A. Find of four of the following: dx 1. y = x sin-1 x +v1– x² 2. y = (x2 + 2x) tanh(x + 1) 3. y…

A: See the details solution in below

Q: Let y = y(t) be the solution to the initial value problem dy – y = e' cos t; y(0} = 1. dt Find the…

A: Given that y=y(t) be the solution to the initial value problem  To find the value of y(pi)

Q: Find the valve of k so that (2y sın x cos x -y + 2 y e** ) dx - (x - sın' x + kxye*) dy 0 becomes…

A:

Q: Find a solution to the initial value problem y' + sin(t)y = g(t), y(0) = 9, that is continuous on…

A: We have to solve this initial value problem:

Q: Given that x(t) = c¡ cos wt + cz sin wt is the general solution of x" + w²x = 0 on the interval (-*,…

A: 10 Given solution of differential equation is x(t)=c1cos ωt+c2 sinωt of the differential equation…

Q: Consider the initial value problem y′=cos(5πt),y(0)=1.Determine a value of h to ensure that the…

A:

Q: The steady state temperature distribution on a thin metal is given by the Laplace equation dx2 ду?…

A:

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: (a) The temperature distribution u(x, t) of the one-dimensional silver rod is governed by the heat…

A:

Q: The temperature distribution of a long, thin aluminium rod with a length of 12 cm can be determined…

A: The heat equation k∂2u∂x2=∂u∂t---1 is given with k=0.835cm2s-1, ∆x=2cm, ∆t=0.1s, t≥0. The B.C's are…

Q: The displacement of a structure is defined by the following equation for a damped oscillation: y=9e…

A: The displacement of a structure is defined by the equation  y=9e-0.7tcos4t…

Q: Consider the heat problem that is described by: 0.9urr = Ut, 0 0 u(0, t) = 0, u(5, t) = 0, t>0 u(x,…

A:

Q: Use Euler's method to calculate the first three approximations to the given initial value problem…

A: Given that        y' = 4xex^4 , y(1)=3 , dx = 0.1 By using Euler's method we have to calculate the…

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: Find the temperature u(x.1) from the heat equation in a laterally insulated copper bar 80cm cm long…

A:

Q: Find an explicit solution of the given initial-value problem, and define the exact interval I of the…

A:

Q: Let y = y(t) be the solution to the initial value problem dy y = e' cos t; dt y(0) = 1. - Find the…

A: Given: Initial value problem dydt-y=et cost,   y(0)=1

Q: Suppose that T is to be found from the formula T = x (ey + e-y), where x and y are found to be 2 and…

A:

Q: dy 1; find dt dx at x =- dt Related Rates: Given y = cOs x + sin and 4

A:

Q: If I have 2 for the degrees of freedom with an alpha of 0.05, what would be the critical value of t?

A: we have given that  degree of freedom ( df )= 2  level of significance (alpha)=0.05

Q: Find the temperature u(x, t) in a rod of length L if the initial temperature is f(x)throughout and…

A:

Q: B) Find the distance traveled by the particle P (x.y) between t = 0 and t 4 if the position at time…

A:

Q: Q2: Suppose the electric potential at (x, y) is given by f(x, y) = 0.5 Ln(x² + y²) estimate the…

A: In this question, we have to find the error in f(x,y) and percent relative error for the given value…

Q: 2. Given the joint pdf of X and Y, fxx(x, y) = { '0" (4xy 0<x< y <1 other wise Find the marginal…

A:

Q: Use Euler's method with h = 0.25 to solve the following initial-value problem over the interval from…

A: As per the question we are given a first order differential equation as : dy/dx = yx2 - 1.1y With…

Q: 1. Find the general antiderivative. A. S 5x8 4x4 + 10x3 – x² – 9x + 15 dx В. /2 - cos x + sec x ·…

A:

Q: Find the function f(x) described by the given initial value problem. f'(x) = sin x, f(0) = -6 f(x) =

A: This question is based on application of integration.

Q: dy _ 2y = x-'y¯1 y(1)= 3 dx

A:

Q: Solve the following initial value problem for y: dy +e=2#, y(0) = 0 -2x COS dx

A:

Q: 4. Show that :| f(t) sin a(x – t)dt Y : solves the initial value problem dy +a²y = f(x), dx? dy 0…

A: Below is the answer

Q: Find the function f(x) described by the given initial value problem. f'(x) = sin r, f(0) = 3 = sin…

A: NOTE: Refresh your page if you can't see any equations. . take integration  .................(1)

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: 7. Given a set of N concentration measurements C, at times t, set up the formulas for numerically…

A: We will solve this question using basic knowledge of trapezoidal rule only. Recall that for some "n"…

Q: 1) Find the solution of the following equation: y"+ ly 0, with y (0) = 3 and'y (0) = 3 with A<0. Is…

A: Let λ=-a2&lt;0 Then, y"+λy=0 ⇒y"-a2y=0 Auxiliary equation is m2-a2=0 ⇒m=±a So, the general solution…

Q: In the given DE, cos x + In y+ 0, integrating M (x, y) with respect to x generates a function g (y).…

A: To solve the following differential equation

Q: At the time of t = 0 at 15 cm length (Δx=3 cm, Δt=0.4 s), one side of the rod is contacted with two…

A: This question is about application of integration

Q: use the integrating-factor method

A:

Q: Find a solution to the initial value problem that is continuous on the interval [0, 2π] where sin(t)…

A:

Q: In the given DE, cos x + In y + ( + ev = 0, integrating the coefficient of dx, M (x, y), with…

A: We will find the g(y) as shown below

Q: 4.1. Derive the heat equation with a metal rod with variable cross-sectional area A(x). Using the…

A: Cross section area of metal rod is Ax. Energy density per unit volume is hx,t. Energy in the…