Calculate the Euler method approximation to the solution of the initial value problem at the given...

Calculate the Euler method approximation to the solution of the initial value problem at the given x-values. Compare your results to the exact solution at these x-values.

y' = y+y^2; y(1) = -1, x = 1.2, 1.4, 1.6, 1.8

Expert Solution

Colby Messinger answered 1 year ago

For the initial-value problem, ?'(?) = ?? sin(5?) , ?(0) = 0.5, Use the Euler Method...

For the initial-value problem, ?'(?) = ?? sin(5?) , ?(0) = 0.5, Use the Euler Method with step size of 0.1 to calculate the approximate solution for the differential equation for the initial condition y(0) = 0.5 and plot the result on the direction field graph you produced in paragraph 1. Then do the same for the results of using the Euler Method with step sizes of 0.01 and then 0.005. For the initial-value problem in paragraph 2 above, ?'(?)...

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

Use the method of Undetermined Coefficients to find the solution of the initial value value problem:...

Use the method of Undetermined Coefficients to find the solution of the initial value value problem: y'' + 8y' + 20y = 9cos(2t) - 18e-4t, y(0) = 5. y'(0) = 0

1) Find the solution of the given initial value problem and describe the behavior of the...

1) Find the solution of the given initial value problem and describe the behavior of the solution as t → +∞ y" + 4y' + 3y = 0, y(0) = 2, y'(0) = −1. 2) Find a differential equation whose general solution is Y=c1e2t + c2e-3t 3) Determine the longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution. Do not attempt to find the solution t(t − 4)y" + 3ty' + 4y...

use the method of order two to approximate the solution to the following initial value problem...

use the method of order two to approximate the solution to the following initial value problem y'=e^(t-y),0<=t<=1, y(0)=1, with h=0.5

Compute, by Euler’s method, an approximate solution to the following initial value problem for h =...

Compute, by Euler’s method, an approximate solution to the following initial value problem for h = 1/8 : y’ = t − y , y(0) = 2 ; y(t) = 3e^(−t) + t − 1 . Find the maximum error over [0, 1] interval.

Apply Euler's method twice to approximate the solution to the initial value problem on the interval...

Apply Euler's method twice to approximate the solution to the initial value problem on the interval [0, .5], first with step size h=0.25, then with step size h= 0.1. Compare the three-decimal place values of the two approximations at x=.5 with the value of y(.5) of the actual solution. y'=y-3x-6, y(0)=8, y(x)=9+3x-ex a.) The Euler approximation when h=0.25 of y(.5) is: b.)The Euler approximation when h=0.1 of y(.5) is:

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Calculate the Euler method approximation to the solution of the initial value problem at the given...

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