6. A thin homogeneous metal bar of length 20cm. and made of material with thermal diffusivity 5cmls has insulated ends and lateral sides. The bar has initial temperature in (C°) given by u( x, 0) = 10+ 4x 0

Q: (a) Use the method of characteristics to solve the following boundary-value problem: - yur(x, y) =…

A:

Q: 6. A thin homogeneous metal bar of length 20cm. and made of material with thermal diffusivity 5cm/s…

A:

Q: A 3 cm length silver bar with a constant cross section area 1 cm (density 10 g/cm, thermal…

A:

Q: Consider the IVP dy/dt = (2-t)/(y+2) where y(0)=1.  Find a formula for the solution. State the…

A: In this question, we find a formula for the solution. i.e. y(t) State the domain of the definition…

Q: Problem 12 The volume of the solid obtained by rotating the region bounded by y=(x^2), y=5x   about…

A:

Q: 4. A model for the population of pigeons in the United States is given by the autonomous DE: Р' %3…

A: Since you have posted the multiple parts. I am answering the first three parts. Please post…

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

A:

Q: 3. Find the solution of the initial boundary value problem (IBVP) Un = Ux for -0 0 (x,0) = xsin(x),…

A:

Q: 6. Solve the boundary value problem, or show that it has no solution: П y" – 4y = sin(x), y (0) = 0;…

A:

Q: 11. An ideal elastic string of length L is fixed at its right end, but its left end is attached to a…

A: The given problem is to find the solution for the given wave equation partial differential equation…

Q: 5. Usa the substituti on U(X, 1) = X(x) 7(1) and saparation of varlables to solve the partial…

A: (5). Given, the partial differential equation,                   utt=ux…

Q: The steady state heat conduction over a thin plate is governed by the partial diffe equation: ôx² '…

A:

Q: How we can obtain the numerical solution of the nonlinear boundary value problem y" = y²y', 0≤t≤1…

A: Given y''=y2y', 0≤t≤1y0=0, y1=0 and t0=0, t1, t2, t3, t4, t5=1

Q: 6. Consider the problem u; + u2ux = 0, x 0 satisfying the initial %3D condition u(x,0) = %3D a. Find…

A: Given: Let us consider the problem ut+u2ux=0,x<∞,t>0 in which the initial condition…

Q: Use the method of Green's functions to solve the boundary value problem y" = -x?, y(0) + y'(0) = 4,…

A: The initial differential equation given is as follows: y''=-x2,  y0+y'0=4, y'1=2 Integrate both…

Q: Use Finite-Difference method to approximate the solution of the BVP boundary value problem y" – 3y'…

A: Given,  y''-3y'+4y=sin x, y(0)=9.8, yπ4=15.9  We Use the following approximations,…

Q: Sometimes a constant equilibrium solution has the property that solutions lying on one side of the…

A: Given:

Q: 1st Case (IBVP Summary) (ut = 1.5Uxx, 0≤x≤ 6ft, t> 0 ux(0,t) = 0, ux(6 ft,t) = 0, t> 0 (u(x,0) =…

A:

Q: Find the non trivial solution of advection diffusion boundary value problems ut = uxx-2ux , t>=0,…

A: Given equation is, ut=uxx-2ux, t≥0, 0≤x≤1 u0,t=u1,t=0, t≥0 Take u(x,t)=XxTt Then…

Q: 6. Minimize the material needed to create an open box with dimensions xyz and a volume of 108 in?.…

A:

Q: Consider diffusion in a finite layer of depth L with concentration Co at x=0 and Cat x=L with…

A: As per given data:u0,t=c0 and uL,t=c1Letwx=Ax+Bw0=B⇒B=c0wL=AL+B=c1⇒A=c1-c0LSo,that wx=c1-c0Lx+c0.

Q: Problem 11 The volume of the solid obtained by rotating the region bounded by y=(x^2), y=4x, about…

A:

Q: Consider the system dx dy (4 – 2)(y – 2), dt = y(4 – 3x – x²) dt a) Find all the critical points…

A: Given system is dxdt=4-xy-xdydt=y4-3x-x2

Q: Exercise (2) - Solve using paper solution. d²y dy 2- - y + x = 0 dx² dx Solve using…

A: Find your answer below

Q: 6. Consider the problem u; + u²ux = 0, |x| 0 satisfying the initial condition u(x,0) = %3D 1+x2 a.…

A: The complete solutions are given below

Q: 1st Case (IBVP Summary) ut = 1.5uxx, 0≤x≤ 6 ft, t>0 ux(0, t) = 0, ux(6 ft, t) = 0, t > 0 (u(x,0) =…

A: please comment if you need any clarification. I done lots work for you.. please put thumbs up.thank…

Q: 6. Show that y(x) = Inx is a solution of xy" +y' = 0 on interval (0, 00) but is not a solution on…

A:

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: 2- Find the solution of the partial differential equation =u, -2 with boundary conditions u(x,0) 0…

A:

Q: Problem 10 The volume of the solid obtained by rotating the region bounded by y=(x^2), y=3x  about…

A:

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

A: Find out the value of I after 1.5 seconds.

Q: 3. A thermally conducting solid bounded by two concentric spheres of radii a and b, a<b, is such…

A: Given that the temperature of the inner surface is T1 The temperature of the outer surface is…

Q: 1st Case A 6-ft long rod (laterally insulated) has a thermal diffusivity of 1.5 ft2/hr and initial…

A: For (1), Let us first create the system in both cases and then we will be finding the general…

Q: Find a strict Liapunov function for the equilibrium point (0,0) of x = -2x – y y = -y– x. Find 8>0…

A: Given :-  A strict Liapunov function for the equilibrium point (0,0) of  x’ = -2x-y2 y' = -y-x2 To…

Q: Consider the boundary value problem, 0<x< 0<y< 2 0 < y< ax2 ay2 u(0, y) = y² – 1, u y) = 0, 0<y<…

A: The partial differential equation given is as follows: ∂2u∂x2+∂2u∂y2=0 We are asked to find the…

Q: 26. If 4h = kM², show that typical solution curves look as illustrated in Fig. 2.2.14. Thus if xo 2…

A:

Q: The dynamics of the variable ywith respect to variable xis described by the following stiff ODE: dy…

A:

Q: The dynamics of the variable y with respect to variable x is described by the following ODE: dy –x²y…

A: Runga-Kutta Method of order 4:

Q: Use Euler's method with step size h = 0.2 to approximate the solution to the initial value probler…

A:

Q: 1.) Use the following methods to solve the boundary value problem: - 2- y +x = 0 dx2 with boundary…

A:

Q: Consider the Initial Value Problem (IVT) dy = Axy, y(0) = 1, da where A is a positive constant. The…

A: As per the rules we can solve only 3 subparts. Please check the below answers

Q: Let u (x, t) be the solution of the initial-boundary value problem Ut 0 0, Uz (0, t) = uz (4, t) =…

A:

Q: The heat distribution of a long thin rod can be determined by given heat- conduction equation aT OT…

A: In this problem, different conditions are given in the diagram and in the question. so anyone must…

Q: 3. Using the Fourier transform method solve the heat diffusion PDE equation - = 0 with initial…

A: Given heat diffusion equation is ∂2u∂x2-∂u∂t=0 or ∂u∂t-∂2u∂x2=0                     (1) with initial…

Q: use Euler’s method to calculate the first threeapproximations to the given initial value problem for…

A: y'=y21+2x,y-1=1 and dx=0.5. Use Euler’s method to calculate the first three approximations to the…

Q: Given function f(x,y) = 1 + xy – x - y. a) using partial differential involving limits to obtain…

A: Critical points of a function f(x, y) is given by,  fx(x,y)=0andfy(x,y)=0 Now if (a, b) is any…

Q: Question. No 2. (B). Find the solution of Initial and Boundary value Problem (IVBP) u,(x,t) =…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.