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
Serggg [28]
3 years ago
10

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) = 3. (Round your answer to four decimal places.)
Mathematics
1 answer:
irina [24]3 years ago
4 0

Answer:

Therefore the value of y(1)= 0.9152.

Step-by-step explanation:

According to the Euler's method

y(x+h)≈ y(x) + hy'(x) ....(1)

Given that y(0) =3 and step size (h) = 0.2.

y'(x)= x^2y(x)-\frac12y^2(x)

Putting the value of y'(x) in equation (1)

y(x+h)\approx y(x) +h(x^2y(x)-\frac12y^2(x))

Substituting x =0 and h= 0.2

y(0+0.2)\approx y(0)+0.2[0\times y(0)-\frac12 (y(0))^2]

\Rightarrow y(0.2)\approx 3+0.2[-\frac12 \times3]    [∵ y(0) =3 ]

\Rightarrow y(0.2)\approx 2.7

Substituting x =0.2 and h= 0.2

y(0.2+0.2)\approx y(0.2)+0.2[(0.2)^2\times y(0.2)-\frac12 (y(0.2))^2]

\Rightarrow y(0.4)\approx  2.7+0.2[(0.2)^2\times 2.7- \frac12(2.7)^2]

\Rightarrow y(0.4)\approx 1.9926

Substituting x =0.4 and h= 0.2

y(0.4+0.2)\approx y(0.4)+0.2[(0.4)^2\times y(0.4)-\frac12 (y(0.4))^2]

\Rightarrow y(0.6)\approx  1.9926+0.2[(0.4)^2\times 1.9926- \frac12(1.9926)^2]

\Rightarrow y(0.6)\approx 1.6593

Substituting x =0.6 and h= 0.2

y(0.6+0.2)\approx y(0.6)+0.2[(0.6)^2\times y(0.6)-\frac12 (y(0.6))^2]

\Rightarrow y(0.8)\approx  1.6593+0.2[(0.6)^2\times 1.6593- \frac12(1.6593)^2]

\Rightarrow y(0.6)\approx 0.8800

Substituting x =0.8 and h= 0.2

y(0.8+0.2)\approx y(0.8)+0.2[(0.8)^2\times y(0.8)-\frac12 (y(0.8))^2]

\Rightarrow y(1.0)\approx  0.8800+0.2[(0.8)^2\times 0.8800- \frac12(0.8800)^2]

\Rightarrow y(1.0)\approx 0.9152

Therefore the value of y(1)= 0.9152.

You might be interested in
Please find answer. ​
melisa1 [442]

Answer: (x 1 ,y 1)=(2,3) and (x 2,y 2)=(4,7)by midpoint formula, coordinates of mid point =( 2x 1+x 2, 2y 1 +y 2)=( 22+4, 23+7 )=( 26 , 210)=(3,5).

Step-by-step explanation: Hope this helps

4 0
3 years ago
Read 2 more answers
Which of these could be the graph of F(x) = In x + 1?
bezimeni [28]

Answer:

A

Step-by-step explanation:

rlykydlydlysl6sl6sl6dylsl6sl6dlu

5 0
3 years ago
Find the lcd of the three rational expressions​
Tom [10]
The least common denominator is C!

Hope this helps you! :)
5 0
3 years ago
Find the 14" term<br> 7, 14, 28, 56,
Pavlova-9 [17]

Step-by-step explanation:

it seems we are dealing with multiplication, as the distances between the numbers get bigger and bigger.

and then I see

7 × 2 = 14

14 × 2 = 28

28 × 2 = 56

ok, so the sequence is created by always multiplying by 2.

a1 = 7

a2 = a1 × 2 = 7 × 2 = 14

a3 = a2 × 2 = a1 × 2 × 2 = 7 × 2 × 2 = 28

an = an-1 × 2 = a1 × 2^(n-1) = 7 × 2^(n-1)

a14 = 7 × 2¹³ = 7 × 8192 = 57,344

5 0
2 years ago
Peter jogged 96 yards in 40 seconds? What is his speed in feet per second?
Arturiano [62]
96 yards = 288 feet
speed is 288/40 - 7.2 feet/s
8 0
3 years ago
Read 2 more answers
Other questions:
  • How many sides does a parallelogram have?
    5·1 answer
  • A survey of 1,000 men and women asked, "Do you earn over $50,000 per year?" The table below shows the responses for males and fe
    14·2 answers
  • After 5 minutes of a basketball game
    5·2 answers
  • Which ratio forms a proportion with 18/27 ?
    5·1 answer
  • Find the measure of angle x in the figure below:<br> a. 15<br> b. 25<br> c. 30<br> d. 60
    8·2 answers
  • A fair six sided die is rolled 10 times. What is the chance that we never see a 6
    14·1 answer
  • Can someone pls help me ‼️‼️‼️
    12·2 answers
  • One hundred families each have $2$ fish. Each fish has either one stripe or two stripes. In total, there are $273$ stripes. How
    13·1 answer
  • There is a picture. could you please help?​
    6·1 answer
  • Eric was rock climbing. At one point, he stopped and climbed straight down 2\dfrac{1}{2}2
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!