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
Ile to 2 +2 nie piszcze nic tylko sprawdzam
Bumek [7]

Answer:

Could you rewrite this question in english so we can understand what is being asked? Thank you!

Step-by-step explanation:

6 0
3 years ago
Use the three steps to solve the problem.
Flauer [41]

The two numbers are 8,13.

Step-by-step explanation:

Let,

smaller number = x

Larger number = x+5

According to given statement;

Smaller number + Bigger number = 3x-3

x+(x+5)=3x-3\\x+x+5=3x-3\\2x+5+3=3x\\8 = 3x-2x\\8=x\\x=8

Smaller number = 8

Larger number = 8+5 = 13

The two numbers are 8,13.

Keywords: algebraic equation, addition

Learn more about addition at:

  • brainly.com/question/11229113
  • brainly.com/question/11234838

#LearnwithBrainly

7 0
3 years ago
Read 2 more answers
Somebody pls help me with this question pls
monitta
292in^3
3x6x10=180 because I’ve split the shape in half
7x4x4=112
180+112=292
4 0
2 years ago
Andy was given data to draw 3 scatter diagrams.
vredina [299]

Answer:

A) Negative Correlation. B) C. C) B

Step-by-step explanation:

<h2>A:</h2>

As the line of best fit is travelling downwards, it is a negative correlation, if the line of best fit is travelling upwards, it is a positive correlation, if the points on the graph are all over the place, there is no correlation.

<h2>B:</h2>

As there are only three types of correlation, the strongest is always the positive.

<h2>C:</h2>

The answer is B because there is no correlation and that means that there shouldn't be a line of best fit.

6 0
2 years ago
Place decimal points in 34, 4, and 417 so that the sum of the three numbers is 7.97.
KIM [24]
3.4+0.4+4.17=7.97 you just have to try different combinations of different numbers with the decimals.
                                                             





8 0
3 years ago
Other questions:
  • 2x-8/x^2<br> what is the range of this function ?
    13·1 answer
  • A circle has the radius of 4 cm. Find the length s of the arc intercepted by a central angle of pie/4 radians.
    7·1 answer
  • Mr. Mandel gave his class 12 minutes to read. 5 1/2 pages in that time. At what rate, in pages per hour, did Claire read?
    10·1 answer
  • PLEASE HELP QUICKKKKKKKKKKK
    6·1 answer
  • The formula for the slant height of a cone is I= s-π(pie)r^2 over π(pie) , where S is surface area of the cone. Use the formula
    11·2 answers
  • give the probability that three rolls of a single die will show a 3 on the first roll, a 6 on the second roll and a 5 or 6 on th
    5·1 answer
  • What is the fractional equivalent of 0.2323...?
    15·1 answer
  • 2. Determine whether each table of values represents a linear function. If so write the function. If not, explain why.
    15·1 answer
  • A company sells widgets. The amount of profit , ymade by the company, is related to the selling price of each widget, x, by the
    11·1 answer
  • SOMEONE HELP ME BEFORE I PASS OUT<br><br> 1. |X|≤8<br><br> 2. |X|≤27
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!