Question

Consider the initial value problem given below.

y' = (x+y+1)^{2} , y(0)= -1

The solution to this initial value problem crosses the x-axis at a point in the interval [0, 1.4]. By experimenting with the improved Euler's method subroutine, determine this point to two decimal points.

Answer #1

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Consider the initial value problem given below.
y' = 4sin(x+y), y(0)=2
By experimenting with the improved Euler's method subroutine,
find the maximum value over the interval [0,2] of the solution to
the initial value problem. Where does this maximum value occur?
Give answers to two decimal places.

Consider the initial value problem
dy dx
=
1−2x 2y
, y(0) = − √2
(a) (6 points) Find the explicit solution to the initial value
problem.
(b) (3 points) Determine the interval in which the solution is
deﬁned.

Use Euler's method to approximate y(0.7), where y(x) is the
solution of the initial-value problem y'' − (2x + 1)y = 1, y(0) =
3, y'(0) = 1. First use one step with h = 0.7. (Round your answer
to
two decimal places.) y(0.7) = ? Then repeat the calculations
using two steps with h = 0.35. (Round your answers to two decimal
places.) y(0.35) = ? y(0.7) =?

Use Euler's method to approximate y(1.2), where
y(x) is the solution of the initial-value
problem
x2y'' − 2xy' + 2y = 0, y(1) =
9, y'(1) = 9,
where
x > 0.
Use
h = 0.1.
Find the analytic solution of the problem, and compare the
actual value of y(1.2) with y2. (Round
your answers to four decimal places.)
y(1.2)
≈
(Euler approximation)
y(1.2)
=
(exact value)

Consider the following initial value problem:
dy/dt = -3 - 2 *
t2, y(0) = 2
With the use of Euler's method, we would like to find an
approximate solution with the step size h = 0.05 .
What is the approximation of y
(0.2)?

Use Euler's method to approximate y(0.2), where
y(x) is the solution of the initial-value
problem
y'' − 4y' + 4y = 0, y(0) = −3, y'(0) =
1.
Use
h = 0.1.
Find the analytic solution of the problem, and compare the
actual value of y(0.2) with y2. (Round
your answers to four decimal places.)
y(0.2)
≈
(Euler approximation)
y(0.2)
=
-2.3869
(exact value)
I'm looking for the Euler approximation number, thanks.

Use Euler's method with step size h=0.2 to approximate the
solution to the initial value problem at the points x=4.2 4.4 4.6
4.8 round to two decimal
y'=3/x(y^2+y), y(4)=1

What is the solution to the initial value problem below?
y′=7ex+7x3+x+3
y(0)=2

1. Consider the initial value problem dy/dx =3cos(x^2) with
y(0)=2.
(a) Use two steps of Euler’s method with h=0.5 to approximate
the value of y(0.5), y(1) to 4 decimal places.
b) Use four steps of Euler’s method with h=0.25, to
approximate the value of y(0.25),y(0.75),y(1), to 4 decimal places.
(c) What is the difference between the two results of Euler’s
method, to two decimal places?

Consider the initial value problem
dy/dx= 6xy2 y(0)=1
a) Solve the initial value problem explicitly
b) Use eulers method with change in x = 0.25 to estimate y(1)
for the initial value problem
c) Use your exact solution in (a) and your approximate answer in
(b) to compute the error in your approximation of y(1)

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