Use Euler's method with the given step size to estimate y(1.4) where y(x) is the solution...

Use Euler's method with the given step size to estimate y(1.4) where y(x) is the solution of the initial-value problem y′=x−xy ,y(1)=3.

Expert Solution

Colby Messinger answered 8 months ago

Use Euler's method with step size 0.2 to estimate y(0.4), where y(x) is the solution of the...

Use Euler's method with step size 0.2 to estimate y(0.4), where y(x) is the solution of the initial-value problem y' = 3x − 4xy, y(0) = 0. (Round your answer to four decimal places.) y(0.4) = (b) Repeat part (a) with step size 0.1. (Round your answer to four decimal places.) y(0.4) =

Use Euler's Method with step size 0.11 to approximate y (0.55) for the solution of the...

Use Euler's Method with step size 0.11 to approximate y (0.55) for the solution of the initial value problem y ′ = x − y, and y (0)= 1.2 What is y (0.55)? (Keep four decimal places.)

Use Euler's method with each of the following step sizes to estimate the value of y(0.8),...

Use Euler's method with each of the following step sizes to estimate the value of y(0.8), where y is the solution of the initial-value problem: y' = y, y(0) = 5. (i) h = 0.8 y(0.8) = 9 (ii) h = 0.4 y(0.8) = 9.8 (iii) h = 0.2 y(0.8) = ? The error in Euler's method is the difference between the exact value and the approximate value. Find the errors made in part (a) in using Euler's method to estimate...

Use Euler's method with step size 0.5 to compute the approximate y-values y1, y2, y3 and...

Use Euler's method with step size 0.5 to compute the approximate y-values y1, y2, y3 and y4 of the solution of the initial-value problem. y' = y − 5x, y(3) = 1. y1 = ______ y2 =______ y3 =_______ y4=________ Please show all work, neatly, line by line and justify steps so that I can learn. Thank you!

Exercise (a) Use Euler's method with each of the following step sizes to estimate the value...

Exercise (a) Use Euler's method with each of the following step sizes to estimate the value of y(1.6), where y is the solution of the initial-value problem y' = y, y(0) = 6. (i) h = 1.6 (ii) h = 0.8 (iii) h = 0.4 Exercise (b) We know that the exact solution of the initial-value problem in part (a) is y = 6ex. Draw, as accurately as you can, the graph of y = 6ex, 0 ≤ x ≤ 1.6, together with...

1. Use Euler's method with step size 0.50.5 to compute the approximate yy-values y1≈y(0.5), y2≈y(1),y3≈y(1.5), and...

1. Use Euler's method with step size 0.50.5 to compute the approximate yy-values y1≈y(0.5), y2≈y(1),y3≈y(1.5), and y4≈y(2) of the solution of the initial-value problem y′=1+3x−2y, y(0)=2. y1= y2= y3= y4= 2. Consider the differential equation dy/dx=6x, with initial condition y(0)=3 A. Use Euler's method with two steps to estimate y when x=1: y(1)≈ (Be sure not to round your calculations at each step!) Now use four steps: y(1)≈ B. What is the solution to this differential equation (with the given initial...

Let y′=y(4−ty) and y(0)=0.85. Use Euler's method to find approximate values of the solution of the...

Let y′=y(4−ty) and y(0)=0.85. Use Euler's method to find approximate values of the solution of the given initial value problem at t=0.5,1,1.5,2,2.5, and 3 with h=0.05. Carry out all calculations exactly and round the final answers to six decimal places.

Consider the initial value problem given below. y'=x+4cos(xy), Y(0)=0 Use the improved Euler's method subroutine with...

Consider the initial value problem given below. y'=x+4cos(xy), Y(0)=0 Use the improved Euler's method subroutine with step size h=0.3 to approximate the solution to the initial value problem at points x= 0.0,0.3,0.6.....3.0

Use Euler's Method to make a table of values for the approximate solution of the differential...

Use Euler's Method to make a table of values for the approximate solution of the differential equation with the specified initial value. Use n steps of size h. (Round your answers to six decimal places.) y' = 10x – 3y, y(0) = 7, n = 10, h = 0.05 n xn yn 0 1 2 3 4 5 6 7 8 9 10

Use eulers Method with step size h=.01 to approximate the solution to the initial value problem...

Use eulers Method with step size h=.01 to approximate the solution to the initial value problem y'=2x-y^2, y(6)=0 at the points x=6.1, 6.2, 6.3, 6.4, 6.5

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