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.

Expert Solution

Colby Messinger answered 2 years ago

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 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.)

Suppose that y′=0.162sin2(ty)+1. Plot y(t) from t=0 to t=4 with y(0)=1.286 using Euler's method with a...

Suppose that y′=0.162sin2(ty)+1. Plot y(t) from t=0 to t=4 with y(0)=1.286 using Euler's method with a step size of 0.4.

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!

Use Eulers method to find approximate values of the solution of the given initial value problem...

Use Eulers method to find approximate values of the solution of the given initial value problem at T=0.5 with h=0.1. 12. y'=y(3-ty) y(0)=0.5

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...

for y(t) function ty'' - ty' + ty = 0, y(0)= 0 , y'(0)= 1 solve...

for y(t) function ty'' - ty' + ty = 0, y(0)= 0 , y'(0)= 1 solve this initial value problem by using Laplace Transform. (The equation could have been given such as "y'' - y' + y = 0" but it is not. Please, be careful and solve this question step by step.) )

In each of problems 1 through 4: (a) Find approximate values of the solution of the...

In each of problems 1 through 4: (a) Find approximate values of the solution of the given initialvalue problem at t=0.1, 0.2, 0.3, and 0.4 using the Euler methodwith h=0.1 (b) Repeat part (a) with h=0.05. Compare the results with thosefound in (a) (c) Repeat part (a) with h=0.025. Compare the results with thosefound in (a) and (b). (d) Find the solution y=φ(t) of the given problem and evaluateφ(t) at t=0.1, 0.2, 0.3, and 0.4. Compare these values with the...

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 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.

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