Let y(t) be the solution to y˙=3te−y satisfying y(0)=3 . (a) use euler's method with time step h=0.2 to approximate y(0.2),y(0.(1.0) . k tk yk 0 0 3 1 0.2 equation editor equation editor 2 0.4 equation editor equation editor 3 0.6 equation editor equation editor 4 0.8 equation editor equation editor 5 1.0 equation editor equation editor (b) use separation of variables to find y(t) exactly. y(t) = equation editor equation editor (c) compute the error in the approximations to y(0.2),y(0.6) , and y(1). |y(0.2)−y1|=

Step-by-step explanation:

Point a:

The Euler's method states that:

where

We have that , , ,

So you need to:

So you need to:

The Euler's Method is detailed in the following table.

Point b:

To find the general solution of you need to:

Rewrite in the form of a first order separable ODE:

Integrate each side:

We know the initial condition y(0) = 3, we are going to use it to find the value of

So we have:

Solving for y we get:

Point c:

To compute the error in the approximations y(0.2), y(0.6), and y(1) you need to:

Find the values y(0.2), y(0.6), and y(1) using

Next, where are from the table.

b

step-by-step explanation:

the total is 23.97. 0.25% is off so you have to subtracting 25% from 100% and you will get 75% if you convert it to decimal you will get 0.75. you have to find the original because the formula is % times original = total.so you have the total and the % so you just have to plug it in.

15%

step-by-step explanation:

use the table and count the number of guesses that has two correct answers.

the following are two correct answers

10010, 01100, 11000

a total of 3 numbers having 2 correct guesses out of 20 questions.

probability of getting 2 correct guesses = the number of questions getting 2 correct answers / total number of questions.

= 3/20

to convert it into percent multiply by 100, we get

= 3/20 * 100

= 15%

the answer is 15%

you.