2. An initial value problem and its exact solution y(x) are given below. Apply Euler's meutwice to approximate to this solution on the interval [0, ½], first with step size h = 0 25(two steps), then with step size h = 0.1 (five steps). Compare the three-decimal-placevalues of the two approximations at x = 2 with the value y(½) of the actual solution.y' =(1+y?),y(0) = 1; y(x) := tan (x + T)"ехact"approx.h f(xn, Yn)Yn+1Xn+1f(xn Yn)inYnYn+1114

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Answered: 2. An initial value problem and its…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Take b = 5 and c = 2
Q4) Use the Newton- Raphson method, with 1.5 as starting point, to find solution of f(x)= x-2sinx.
Only need parts C and D
Use Euler's method to approximate y(1.8). Start with step size h=0.1, and then use successively smaller step sizes (h=0.01, 0.001, 0.0001, etc.) until successive approximate solution values at x = 1.8 agree rounded off to two decimal places. y'=x² + y²-2. y(0) = 0 The approximate solution values at x = 1.8 begin to agree rounded off to two decimal places between (Type an integer or decimal rounded to two decimal places as needed.) ▾ So, a good approximation of y(1.8) is.
Use a numerical solver and Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. y' = ey, y(0) = 0; y(0.5) y(0.5) y(0.5) (h = 0.1) (h = 0.05)
Given that y = sin x is a solution of y(4) + 2y" + 11y" + 2y' + 10y = 0 Find the general solution of the DE and Plot the graph of it.
The green graph below shows the graph of the solution to 1 5y"+ by' + cy = 0 y(0) = 0, y'(0) = 1 for some particular values of b, c that have b2 – 4ac > 0. - Adjusting the sliders for b and c will show you different solutions to this equation in red. Use them to align the red and green graphs so that the red graph overlays the green one. Note that a red graph may not appears for some combinations of b and c. The point of this exercise is not to solve rigorously, but to understand how changing the values of b and c affects the behavior of the system 4 c = 8 - o + + Į ↑ →
Use Euler's method to approximate y(1.0). Start with step size h = 0.1, and then use successively smaller step sizes (h= 0.01, 0.001, 0.0001, etc.) until successive approximate solution values at x = 1.0 agree rounded off to two decimal places. y' = x² + y² -1, y(0) = 0 The approximate solution values at x = 1.0 begin to agree rounded off to two decimal places between is (Type an integer or decimal rounded to two decimal places as needed.) So, a good approximation of y(1.0) h = 0.001 and h = 0.0001. h = 0.1 and h=0.01. h = 0.01 and h = 0.001.
Use Euler's method to approximate y(1.9). Start with step size h = 0.1, and then use successively smaller step sizes (h = 0.01, 0.001, 0.0001, etc.) until successive approximate solution values at x = 1.9 agree rounded off to two decimal places. y' =x? +y? - 2, y(0) = 0 The approximate solution values at x = 1.9 begin to agree rounded off to two decimal places between h= 0.001 andh= 0.0001. So, a good approximation of y(1.9) is 0.11.
For the solution of the equation x-x-10=0 which lies in the interval [1, 2] use one iteration of the fixed point method x₂ = g(x₁) 2 where g(x)=√x+10 and x₁ = 2 1 expressing your answer correct to 2 decimal places. O 1.81 O 1.77 O 1.86 O 1.58
Given y' = y cost, 0st<1, y(0) = 1 and N=5. Then using Euler's method, the approximation of the solution at t=0.4 ( use 4 digit rounding) Select one: a. 1.2216 b. 1.2145 c. 1.4399 d. 1.4352
Given y' = y cost, 0sts1, y(0) = 1 and N=5. Then using Euler's method, the approximation of the solution at t=0.4 ( use 4 digit rounding) Select one: a. 1.4352 b. 1.4399 с. 1.2216 d. 1.2145

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