Problem 6: (Continuation of the previous problem) Determine the temperature u(x, t) of a 25 cm long metal bar in point x at the moment of time t > 0. The initial temperature is u(x, 0) = = x, when 0 < x < 25 cm, the end points are insulated (there is no flux through the end points) and the material parameter is a² = 1.

Q: 1) Give the Interval of existance for the Solution to the initial valve problem. (+²-16)y" + Cos(4+)…

A:

Q: The steady two-dimensional temperature (7) distribution in an isotropic heat conducting materials is…

A:

Q: Find the particular solution to the equation y'' + 6y' + 9y = e Yp(t) = - 3t arctant

A:

Q: 1. The height of an object of mass 1 kg suspended on a spring whose spring constant is 5 N/m (when…

A:

Q: 3. Use your solution from Part 2 to give solutions to the IVPS i. y" + 2y' + 16y = cos 3t, y(0) =…

A:

Q: Consider a body that moves horizontally through a medium whose resistance is proportional to the…

A: GIVEN: dvdt =-kv2 v(t) = v01 + v0 k t

Q: Find a function y=P(t)that is a solution of y'=.02y with initial condition y=100 when t=0.

A:

Q: find the solution yll +2y' +2y=e-t, y(0)=0, y' (0) =0 -2t e-t +cost a e-t-e-t cost b0 e-t-e-2t +cost…

A:

Q: 2) A population is changing over time at a rate modeled by the function P'(t) = 4te08(1-²) where t…

A:

Q: A 4-pound weight is hung on a spring and stretches it 1 foot. The mass spring system is then put…

A: Draw the figure, which is given below. In equilibrium,  mg−kx0=0⇒mg=kx0 Given, mg=4 and x0=1…

Q: The following initial value problem is shown below: mx"+cx'+kx=F(t), x(0)=0, x'(0)=0 It represents…

A:

Q: c'(x) = e(x) e'(x) = t(x) t'(x) = h(x) h'(x) = c(x) 0 1 2 1 0 4 3 3 4 1 2 لا e(x) c(x) 3 t(x) 4 1 3…

A:

Q: (-1)(*+1) + 1 -sin L NAX sinh (nxy/L) 0(x, y) = Σ n sinh (naW/L) n=1 Using this expression,…

A: Given: Temperature distribution equation is as follows: θx,y=2π∑n=1∞-1n+1+1nsinnπxLsinhnπxLsinhnπWL…

Q: Consider the following initial value problem: Edit y" + 4y' + 20y = d(t – 1); y(0) = 1, y'(0) = 0 a)…

A:

Q: 6. DETAILS ZILLDIFFEQMODAP11 5.1.027.EP. A 1-kilogram mass is attached to a spring whose constant is…

A:

Q: Consider the IVP dy = (). Iy(20 -- y), y(0) = 1. dt %3D (a) Solve the IVP, finding y explicitly as a…

A:

Q: (7) Consider a particle moving along a straight line whose position function is s(x) = 4t - t2,…

A: Consider a particle moving along a straight line whose position function is , where s is in feet and…

Q: Allow y(x) be the solution for the following initial value problem and then find y(e):  dy/dx =…

A:

Q: 2. Solve the following initial Condition Problems: dy а. dx Vry, y(1) = 2. || b. y' = x + y, y(0) =…

A:

Q: Consider the following initial value problem: = sin(y +t) +e - sin(e' +t), y(0) = 2 Show that there…

A: Given the initial value problem, y'=siny+t+et-sinet+t, y0=2   We will make use of the existence and…

Q: Find the answer of the followving initial value problem: 2y" + 5y' - 12y=0, y(0)=1, y'(0)=2

A:

Q: a) A vibrating spring can be modeled by the initial value problem: mx"(t) + bx'(t) + kx(t) = 0 With…

A: