Solve using (a) analytical method, (b) Euler's Method, dy=x²y - 1.1y
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A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…
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- 3. (a) By sketching the graphs of 1 y = In x and y = x2 on the same coordinate system, determine the number of solutions of the equation In x = 2. et-2 has a unique fixed-point in the (b) Show that the function g(x) = interval [1.5, 2]. %3D (c) Use part (i) and (ii) to carry out three iterations to approximate the root of In x =2, starting with po = 1.5.10x1 + 2x2 + X3 = 13 X1 + 10x2 + 2x3 = 13 2x1 + x2 + 10x3 = 13 What is the (x1,X2, X3) values by using Gauss Seidel method for initial value (0,0,0) and 4 iteration. 3.Find the iterative scheme for the root of equation x'+3x -4 = 0 by iteration method near to 1.2. .a 5+x, Xn+1 %3D .b Xy+1 = (5–3x, )% .C 2.x, – x, +6 Xn+1 3 %3D 3x, +1 .d Xn+1 = (4– 3.x, )3
- Compute Manually using Newton Raphson Method with 5 iterations with complete solution#1 Solve the following non-linear equations manually using: a) Bisection Method (5 iterations)Use the Improved Euler method with step size 0.25 to y(x) estimate (1) , where is the solution of the problem y = 1-y-y²³ with initial values y(0) = 0 Make the iterations steps and create the entire table
- 1) Perform 3 iterations to Maximize f(x) = -1.5x6 - 2x¹ + 12x a) Using Golden-Section Search (x₁ = 0, xu = 2) b) Using Newton's Method (xo = 2) LBased on fixed point method, If we have this formula – 2x – 5 = 0 1- Estimate the number of iterations necessary to obtain approximations accurate to within 102, 2- Perform the calculations for x in [2, 3] , if p, = 2 ,g(x)=V2x +5A hand-held calculator will suffice for the Problem. The problem an initial value problem and its exact solution are given. Approximate the values of x(0.2) and y(0.2)in three ways: (a) by the Euler method with two steps of size h = 0.1; (b) by the improved Euler method with a single step of size h = 0.2; and (c) by the Runge–Kutta method with a single step of size h = 0.2. Compare the approximate values with the actual values x(0.2) and y(0.2). x' = 3x - y, x(0) = 2, y' = x + y, y(0) = 1; x(t) = (t+2) e2t, y(t) = (t+1) e2t
- A hand-held calculator will suffice for the Problem. The problem an initial value problem and its exact solution are given. Approximate the values of x(0.2) and y(0.2)in three ways: (a) by the Euler method with two steps of size h = 0.1; (b) by the improved Euler method with a single step of size h = 0.2; and (c) by the Runge–Kutta method with a single step of size h = 0.2. Compare the approximate values with the actual values x(0.2) and y(0.2). x' = 2x + 3y, x(0) = 1, y' = 2x + y, y(0) = -1; x(t) = e-t , y(t) =+ e-tA hand-held calculator will suffice for the Problem. The problem an initial value problem and its exact solution are given. Approximate the values of x(0.2) and y(0.2)in three ways: (a) by the Euler method with two steps of size h = 0.1; (b) by the improved Euler method with a single step of size h = 0.2; and (c) by the Runge–Kutta method with a single step of size h = 0.2. Compare the approximate values with the actual values x(0.2) and y(0.2). x' = 9x + 5y, x(0) = 1, y' = -6x - 2y, y(0) = 0; x(t) = -5e3t + 6e4t, y(t) = 6e3t + 6e4tA hand-held calculator will suffice for the Problem. The problem an initial value problem and its exact solution are given. Approximate the values of x(0.2) and y(0.2)in three ways: (a) by the Euler method with two steps of size h = 0.1; (b) by the improved Euler method with a single step of size h = 0.2; and (c) by the Runge–Kutta method with a single step of size h = 0.2. Compare the approximate values with the actual values x(0.2) and y(0.2). x' = 5x - 9y, x(0) = 0, y' = 2x - y, y(0) = -1; x(t) = 3e2t sin 3t, y(t) = e2t(sin 3t - cos 3t)