1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
rewona [7]
3 years ago
15

Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the initial-value problem y' = x2y − 1 2 y

2, y(0) = 9. (Round your answer to four decimal places.) y(1) = Need Help?
Mathematics
1 answer:
GuDViN [60]3 years ago
7 0

Answer:

Euler's method is a numerical method used in calculus to approximate a particular solution of a differential equation. As a numerical method, we have to apply the same procedure many times, until get the desired result.

In first place, we need to know all the values the problem is giving:

  • The step size is 0.2; h = 0.2. This step size is a periodical increase of the x-variable, which will allow us to calculate each y-value to each x.
  • The problem is asking the solution y(1), which means that we have to find the y-value assigned for x = 1, through the numerical method.
  • The initial condition is y(0) = 9. In other words, x_{o} = 0\\y_{0}=9.

So, if the initial x-value is 0, and the step size is 0.2, the following x-value would be: x_{1}=0.2; then x_{2}=0.4; x_{3} =0.6; x_{4} =0.8;x_{5} =1; and so on.

Now, we have to apply the formula to find each y-value until get the match of x_{5}=1, because the problem asks the solution y(1).

According to the Euler's method:

y_{1} =y_{0} +hF(x_{0};y_{0})\\y_{2} =y_{1} +hF(x_{1};y_{1})\\y_{n} =y_{n-1} +hF(x_{n-1};y_{n-1})

Where F(x;y)=x^{2} y-12y^{2}, and x_{0} =0; y_{0} =9; h=0.2.

Replacing all values we calculate the y-value assigned to x_{1}:

y_{1} =9+0.2((0)^{2} 9-12(9)^{2})=-185.4.

Now, y_{1} =-185.4, x_{1} =0.2; h=0.2. We repeat the process with the new values:

y_{2} =y_{1} +hF(x_{1};y_{1})  \\y_{2} = -185.4+0.2((0.2)^{2} (-185.4)-12(-185.4)^{2} )\\y_{2}=-82682.47

Then, we repeat the same process until get the y-value for x_{5} =1, which is y_{5} = -1.0018, round to four decimal places.

Therefore, y(1)=-1.0018.

You might be interested in
A bowl of fruit punch is made by mixing 3 parts orange juice to 8 parts mango juice. How much mango juice needed to make 715 ml
Morgarella [4.7K]

Answer: 520 ml

Step-by-step explanation : Add 8+3. Then divide 11 into 715. Multiply 65 by 8.

3 0
3 years ago
Tickets to a movie cost $7.25 for adults and $5.50 for students a group of friends purchased 8 tickets for $52.75 how many adult
irina1246 [14]

Answer:

The number of adults tickets and student tickets purchased is 5 and 3.

Given that,

Tickets to a movie cost $7.25 for adults and $5.50 for students.

A group of friends purchased 8 tickets for $52.75.

Here we assume the no of adult tickets and no of student tickets be x and y.

Based on the above information, the calculation is as follows:

7.25x + 5.50y = 52.75 .............(i)

x + y = 8

x = 8 - y..................(2)

Now put the x value in the equation (1)

So,  

7.25(8-y) + 5.50y = 52.75

7.25 × 8 - 7.25y + 5.50y = 52.75

58 - 1.75y = 52.75

5.25 = 1.75y

y = 3

So,  

x = 8 - 3

= 5

Therefore we can conclude that the number of adults tickets and student tickets purchased is 5 and 3.

-Hope this helps<3

4 0
2 years ago
What is 7.03 as a mixed number or fraction in simplest form​
Alona [7]
7.03 can be converted to 7 3/100.

.03 is the equivalent to 3 hundredths, we know this because it in the hundredths place.
5 0
3 years ago
How many kilograms are 0.54 decalitres?
Anarel [89]

Answer:

A measure of capacity or volume in the metric system equal to one-tenth (10-1) of a liter. One deciliter is also equal to 6.1022 cubic inches, or 3.38 fluid ounces

Step-by-step explanation:


4 0
3 years ago
Read 2 more answers
Tex's Taco Truck serves tacos on either hard or soft shells. Yesterday, Tex's Taco Truck sold 5 hard-shell tacos for every 2 sof
Nady [450]

Answer:

65 hard-shells

26 soft shells

Step-by-step explanation:

5 x 13 = 65

2 x 13 = 26

65 - 26 = 39

7 0
2 years ago
Other questions:
  • A survey asked a group of students to choose their favorite type of music from the choices of rock, hip-hop, and country. The re
    7·2 answers
  • 2y + (5+8)=(2y+5+8 is it.True or false
    14·2 answers
  • How to find the length of the third side of a triangle given two sides and an angle are 35 and 70
    13·1 answer
  • Jessica bakes 112 muffins in 7 batches. How many muffins does each batch contain?
    9·2 answers
  • Molly spent 1 hour and 30 minutes swimming 5 laps in the river. If it took her the same time to swim each lap, how long would it
    6·1 answer
  • Find the median and mean of the data wich reflects the best measure of the center
    8·2 answers
  • 3 squares = 27 feet<br> How many feet represent 1 square?
    6·2 answers
  • What is the value of x?
    11·1 answer
  • Determine the slope and y-intercept of the line represented by the equation:<br> 3x – 4y - 16 = 0
    6·2 answers
  • Help I please I will give crown if correct 10points!!!<br><br> Don’t skipppp pleaseee
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!