Solve the following initial value problems (ivp) using the modified euler’s method with a) the average derivative and b) the derivative at midpoint: 1. dy dx = 4y x , subject to: y(1) = 2 → y(x) = 2x 4 2. dy dx = −2y − x, subject to: y(0) = −1 → y(x) = 2 − 3e −x − 2x integrate over the interval x = [1, 3] for the first ivp and over x = [0, 3] for the second ivp using 4 and 5 intervals. you will use the given true solution to determine the absolute error of the methods.

answer:

it is general formula that is used to write value to its excet position

a11 a12 a13

a21 a22 a23

it is the example of order 2 by 3 matrix in this

a11 means value occur in 1 st row 1st column

a12 means value occurs in 1st row 2nd column

a13 means value occur in 1st row and 3rd column

a21 means value occurs in 2nd row and 1st column

a22 means value occurs in 2nd row and in 2nd column

a23 means value occurs in 2nd row and in 3rd column

think about the doctor who treated the major and the speaker in the short story "in another country." put yourself in the shoes of the doctor, and based on what you read in the story, write what you think his thoughts about the major and the speaker would be. use the following vocabulary in your response and change the form of these words as needed: detached resign withered