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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

irina [24]

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.

4 0

3 years ago

"Jeremy runs 7 miles per week and increases his distance by 1 mile each week. Tony runs 3 miles per week and increases his dista

s344n2d4d5 [400]

Make a table graph and go from 0-10 top for weeks and bottom for miles, label one Jeramy and the other one tony. For Jeremy add one mile each week and for timely add to by week 4 they both should have ran 10 miles

5 0

3 years ago

Rationalise the denominator of giving your simplest form 10/4 + square root 6

never [62]

dear brainly

please delete this answer without warning me. I will re-answer this once I get the chance. Thank you.

3 0

3 years ago

Algebra 1A unit 6 lesson 6

AnnyKZ [126]

1. y = -x - 2...slope here is -1. A parallel line will have the same slope

y = mx + b
slope(m) = -1
(2,-2)...x = 2 and y = -2
now we sub and find b, the y int
-2 = -1(2) + b
-2 = -2 + b
-2 + 2 = b
0 = b

so ur parallel equation is : y = -x
=========================
2. -1 = -3/2(2) + b
-1 = -3 + b
-1 + 3 = b
2 = b
parallel equation is : y = -3/2x + 2
==========================
3. parallel equation is : x = 4
==========================
4. 3 = 1/2(-2) + b
3 = -1 + b
3 + 1 = b
4 = b
parallel equation is : y = 1/2x + 4
===========================
5. y + 0 = 2(x - 5)
y = 2x - 10 <== parallel line
============================
6. neither
============================
7. if ur second equation is : 2x + y = 7, then the lines are parallel
============================
8. neither
============================
9. sometimes
============================
10. never

8 0

3 years ago

Read 2 more answers

Sue Has 44 Rib bones on display. there are 22 on the right side and 22 on the left on the right of its body on the right side 9/

Murljashka [212]

Answer:

18/44

Step-by-step explanation:

To turn 9/22 into something over 44, we need to figure out what to multiply it by.

44 / 22 = 2.

Multiply 9/22 by 2:

9/22 * 2 = 18/44

4 0

3 years ago