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
The principal argument of z = —4+i4√3 is​
AnnyKZ [126]

Answer:

Let z=−4+0i. Then, ∣z∣=

(−4)

2

+0

=4

Clearly, the point (−4,0) representing z=−4+0i lies on the negative side of real axis. Therefore, principal argument of z is π.

3 0
3 years ago
HELPPPPPPPPPPP
liubo4ka [24]
<span>(A) Find the approximate length of the plank. Round to the nearest tenth of a foot.
Given that the distance of the ground is 3ft.
In order to get the length of the plank,
we can use the this one.

cos 49 = ground / plank
cos 49 = 3 / plank
plank = cos 49 / 3
plank = 0.10 ft

</span><span>(b) Find the height above the ground where the plank touches the wall. Round to the nearest tenth of a foot.
</span><span>
The remaining angle is equal to
angle = 180 - (90+49)
angle = 41

Finding the height.
tan 41 = height / ground
tan 41 = height / 3
height = tan 41 / 3
height = 0.05 ft.

(A) 0.10 feet
(B) 0.05 feet</span>
3 0
4 years ago
Triangle ABC is similar to triangle DEF solve for r?
Simora [160]

Answer:

send a picture too understand it

Step-by-step explanation:

we dont have enough information

4 0
3 years ago
Please help!!!!!!!!!!! :(((
kykrilka [37]

Answer:

7.5

Step-by-step explanation:

Use pythagorean thereom

5 0
3 years ago
Read 2 more answers
2 1/3 x -1 1/2=? Awarding Brainlyest lol
Nastasia [14]

Answer:

-3.5 or 3 1/2

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • At the frozen treats company they can produce 12,000 popsicles each 4-hour shift.If they have three 4-hour shifts each day,how m
    5·1 answer
  • HELP ASAP!!!!!!!!!!!What figure is a dilation of Figure A by a factor of 3? A quadrilateral labeled figure A. The sides are labe
    8·1 answer
  • I need help pleaces ​
    6·1 answer
  • 2. Decreasing W-4 allowances will ________ the net pay in your paycheck and ______ your total tax burden.
    8·1 answer
  • Cam can bake 144 cakes in 30 minutes. How Many can she bake in 40 mins?
    5·2 answers
  • The change from one number to the next in a geometric sequence is called
    9·1 answer
  • Solve this simultaneous equation? <br><br> 4x + y = 25<br> x - 3y = 16
    13·1 answer
  • Hey I Need Help With This. What Is the answer?<br>​
    7·1 answer
  • Please solve this I need help<br> +
    13·1 answer
  • All of the following factors affect the level of wages except which of the following?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!