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For this problem we will be analyzing the differential equation y'=y-x with the initial condition y(0) = 2. For parts c-d you may use excel to do your computations. (a) Use methods from the course to solve this differential equation exactly. Then Find the value of y(1). (b) Use Euler's Method with a step size h = 0.1 to estimate the value of y(1). (c) Use the Improved Euler's Method with a step size h = 0.1 to estimate the value of y(1). (d) Use the Runga Kutta Method with a step size h = 0.1 to estimate the value of y(1). (e) Which method was the most accurate? What was the error for this method? 

          For this problem we will be analyzing the differential equation y'=y-x with the initial condition y(0) = 2. For parts c-d you may use excel to do your computations.
(a) Use methods from the course to solve this differential equation exactly. Then Find the value of y(1).
(b) Use Euler's Method with a step size h = 0.1 to estimate the value of y(1).
(c) Use the Improved Euler's Method with a step size h = 0.1 to estimate the value of y(1).
(d) Use the Runga Kutta Method with a step size h = 0.1 to estimate the value of y(1).
(e) Which method was the most accurate? What was the error for this method?
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For this problem we will be analyzing the differential equation y'=y-x with the initial condition y(0) = 2. For parts c-d you may use excel to do your computations. (a) Use methods from the course to solve this differential equation exactly. Then Find the value of y(1). (b) Use Euler's Method with a step size h = 0.1 to estimate the value of y(1). (c) Use the Improved Euler's Method with a step size h = 0.1 to estimate the value of y(1). (d) Use the Runga Kutta Method with a step size h = 0.1 to estimate the value of y(1). (e) Which method was the most accurate? What was the error for this method?

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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For this problem, we will be analyzing the differential equation y'' with the initial condition y0=2. For parts c-d, you may use Excel to do your computations. a) Use methods from the course to solve this differential equation exactly. Then, find the value of y(1). b) Use Euler's Method with a step size h=0.1 to estimate the value of y(1). c) Use the Improved Euler's Method with a step size h=0.1 to estimate the value of y(1). d) Use the Runge-Kutta Method with a step size h=0.1 to estimate the value of y(1). e) Which method was the most accurate? What was the error for this method?
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Transcript

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00:01 Hello everyone, we have to solve this differential equation.
00:03 So we have d -y divided by d x is equal to x squared divided by y squared.
00:08 So here we have y -square -d -y is equal to x -square -d -x...
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