Use Euler's method with step size 0.5 to compute the approximate
y-values y1, y2,
y3 and y4 of the solution
of the initial-value problem. y' = y − 5x, y(3) = 1.
y1 = ______
y2 =______
y3 =_______
y4=________
Please show all work, neatly, line by line and justify steps so
that I can learn.
Thank you!
Use Euler's method with step size 0.2 to estimate
y(0.4),
where y(x) is the
solution of the initial-value problem y' =
3x − 4xy,
y(0) = 0. (Round your answer to four decimal
places.)
y(0.4) =
(b) Repeat part (a) with step size 0.1. (Round your answer to four
decimal places.)
y(0.4) =
Let y′=y(4−ty) and y(0)=0.85.
Use Euler's method to find approximate values of the solution of
the given initial value problem at t=0.5,1,1.5,2,2.5, and 3 with
h=0.05.
Carry out all calculations exactly and round the final answers
to six decimal places.
Use
Euler's Method to make a table of values for the approximate
solution of the differential equation with the specified initial
value. Use n steps of
size h. (Round your
answers to six decimal places.)
y' = 10x – 3y, y(0) = 7,
n = 10,
h =
0.05
n
xn
yn
0
1
2
3
4
5
6
7
8
9
10
Use eulers Method with step size h=.01 to approximate the
solution to the initial value problem y'=2x-y^2, y(6)=0 at the
points x=6.1, 6.2, 6.3, 6.4, 6.5
Use Euler's method with each of the following step sizes to
estimate the value of y(0.8), where y is the
solution of the initial-value problem: y' = y,
y(0) = 5.
(i) h = 0.8
y(0.8) = 9
(ii) h = 0.4
y(0.8) = 9.8
(iii)
h = 0.2
y(0.8) = ?
The error in Euler's method is the difference between the exact
value and the approximate value. Find the errors made in part (a)
in using Euler's method to estimate...
Using Runge-Kutta method of order 4 to approximate y(1) with
step size h = 0.1 and h = 0.2 respectively (keep 8 decimals):
dy/dx = x + arctan y, y(0) = 0.
Solutions: when h = 0.1, y(1) = 0.70398191. when h = 0.2, y(1) =
0.70394257.
Exercise (a)
Use Euler's method with each of the following step sizes to
estimate the value of y(1.6), where y is the
solution of the initial-value problem y' = y,
y(0) = 6.
(i) h = 1.6
(ii) h = 0.8
(iii) h = 0.4
Exercise (b)
We know that the exact solution of the initial-value problem in
part (a) is y = 6ex. Draw, as
accurately as you can, the graph of y =
6ex, 0 ≤ x ≤ 1.6, together
with...