Consider the ODE ƒ(x,y) = x – y. Take initial conditions xo = 0, Yo = y(0) = 11, x1 solve for y(30) with a step size of 0.2 using an adaptation of Euler's method, which uses two known y solutions to...


Consider the ODE ƒ(x,y) = x – y. Take initial conditions xo = 0, Yo = y(0) = 11, x1<br>solve for y(30) with a step size of 0.2 using an adaptation of Euler's method, which uses two known y solutions to<br>approximate the next y solution. The general formula is:<br>= 0.2 and y, = y(0.2) = 22,<br>1<br>Yi+2 = Yi+1 +h<br>An example of the first few iterations is shown below.<br>Y2 = y1 + h<br>= 16.5600<br>Y3 = y2 + h<br>= 13.8920<br>Y4 = y3 +h<br>= 11.5204<br>What is the value of y(30) rounded to the nearest integer?<br>Note: Remember to round the final answer.<br>

Extracted text: Consider the ODE ƒ(x,y) = x – y. Take initial conditions xo = 0, Yo = y(0) = 11, x1 solve for y(30) with a step size of 0.2 using an adaptation of Euler's method, which uses two known y solutions to approximate the next y solution. The general formula is: = 0.2 and y, = y(0.2) = 22, 1 Yi+2 = Yi+1 +h An example of the first few iterations is shown below. Y2 = y1 + h = 16.5600 Y3 = y2 + h = 13.8920 Y4 = y3 +h = 11.5204 What is the value of y(30) rounded to the nearest integer? Note: Remember to round the final answer.

Jun 09, 2022
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