I 3. Solve the boundary value problem -u" + xu = 0, using Ritz finite element method with linear piecewise polynomial for three elements of equal length. u(0) + u'(0) = 1, u(1) = 1

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Q: Use the Newton Raphson Method with XO=[-1 -2 1]' to approximate the solution to the given nonlinear…

A: Given a nonlinear system, Let  fx1,x2,x3=x13+x12x2-x2x3+6gx1,x2,x3=ex1+ex2-x3hx1,x2,x3=x22-2x1x3-4…

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A: Given that y''-3y'+2y=0, y1=2, y2=0, h=14

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Q: 6. Use the Euler's method to obtain a MATLAB graph of an approximate solution of the initial dy…

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Q: 1 Obtain a numerical solution of y-1 = using Euler's method with step size equal to (0.02) y and…

A: Given 1yy'-1=x3y

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A: y' = -y , y(0)=1 and h=0.1 f(x,y) = y' = -y  x0 = 0   and  y0 = 1

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A: Given: Initial value problem d3xdt3+d2xdt2(x-t)+dxdt2-x2=0x(0.5)=-1, dxdt(0.5)=1, d2xdt2(0.5)=2 Step…

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A: In this question, we solve the differential equation using initial conditions.

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Q: 15. Find the value(s) of y such that the solution of the initial-value problem y" – 4 y = sin x;…

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Q: 1. a) Use Gauss Seidel Method with X0)=[0 0 0 0]" to approximate the solution to the given linear…

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Q: Use Euler's method with specified step size to determine the solution to the given IVP at the…

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Q: Determine the first three nonzero terms in the Taylor polynomial approximation for the given initial…

A: Given that y'=7siny+2ex and y0=0 So, y'0=7sin0+2e0=2 Now take the derivative for y'=7siny+2ex with…

Q: 5. Use the finite difference method of order two with step size h = 0.25 to solve y" – xy' – xy = 0,…

A: A  finite set is a set that has a finite number of elements. Informally, a finite set is a set in…

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Q: 18- Given with boundary condition y(0) -1.5, y()-0, using 6 equidistant nodes +Sy- cos(3x) - 0 use…

A: The complete solutions are given below

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Q: 2. Find the first three approximations yı, y2, y3 using Euler's method for the initial value problem…

A: Let's find.

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A: To find-  Prove that Mx, y + Nx, ydydx = 0 can be made exact using an integrating factor that…

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Q: The nonlinear system 5a – x3 = 0, x2 – 0.25(sin x1 + cos x2) = 0 has a solution near (, )'. (a) Find…

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A: Solving the 1st question. Given:

Q: 2. (a) Use the method of undetermined coefficient to find the general solution of the non-…

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Q: (a) Find the general solution of the equation (x – 2) y dr 3(х — 1) -y3 1 - (x + 1) (b) Given the…

A: A first-order linear ordinary differential equation(ODE) is of the form y'(x)+p(x)y=q(x). The…

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

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

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Q: 11. Find the general solution of the 2nd order non-homogeneous DE: y" - 2y'- 3y = 4xe a. Methods of…

A: Given that: y''-2y'-3y=4xex

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Q: 3. Use Finite-Difference method to solve the boundary value problem dy dy +x dr+y= 3x² + 4x + 6 dx…

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Q: 3. Find the general solution to the second order nonhomogeneous linear equa- tion y" +y/ - 2y = 6et.

A: To find the particular solution use the method of undetermined coefficients. Since e^t appears in…

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Q: Solve the boundary value problem given as y' y" = 1, x2 - with boundary conditions y' (0.5) =…

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Q: The Euler method for approximating a solution to the first order IVP: y' = x + 3y, y(1) = 0 is Yn+1…

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Q: Solve the boundary-value problem y" + x²y' - 4xy = 2x³ +6x²-2, y(0) = 0, y(1) = 2 by using the…

A: Given that, The boundary value problem, y"+x2y'-4xy=2x3+6x2-2,            1       y0=0, and y1=2. By…

Q: 1. Use the Piecewise Linear Algorithm to approximate the solution to the boundary-value problem + y…

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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: Exer 1. Solve the following first-order boundary value problem 2 u +4 u, + 40 u = u(z, 0) = e* 60…

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Q: 1. Use the method of reduction of order to find a second solution y2(x) and a particular solution…

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Q: 11. Find the general solution of the 2nd order non-homogeneous DE: y" - 2y'- 8y = 2xe* a. Methods of…

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Q: b) Solve the boundary-value problem у" + ху — 2у — 5х 3D х? With the following boundary conditions…

A: (b) Given that y''+xy-2y-5x=x2 Given boundary conditions are, 2y(0)+y'(0)=1 and 2y(2)+2y'(2)=2 at…