Question

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 *y*_{2}. (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.

Answer #1

here is the Euler's approximation.

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)

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

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) =?

a)Program a calculator or computer to use Euler's method to
compute y(1), where y(x) is the solution
of the given initial-value problem. (Give all answers to four
decimal places.)
dy
dx
+ 3x2y =
9x2,
y(0) = 4
h =
1
y(1) =
h =
0.1
y(1) =
h =
0.01
y(1) =
h =
0.001
y(1) =
(b) Verify that
y = 3 +
e−x3
is the exact solution of the differential equation.
y = 3 +
e−x3
⇒ y'...

Use Euler's method with step size 0.2 to estimate y(3), where
y(x) is the solution of the initial-value problem y' = 3 − 3xy,
y(2) = 0. (Round your answer to four decimal places.) y(3) =

Use Euler's method with step size 0.2 to estimate y(0.6) where
y(x) is the solution to the initial value problem y' = y+x^2, y(0)
= 3

4. For the initial-value problem y′(t) = 3 + t − y(t), y(0) =
1:
(i) Find approximate values of the solution at t = 0.1, 0.2,
0.3, and 0.4 using the Euler
method with h = 0.1.
(ii) Repeat part (i) with h = 0.05. Compare the results with
those found in (i).
(iii) Find the exact solution y = y(t) and evaluate y(t) at t =
0.1, 0.2, 0.3, and 0.4. Compare these values with the results of...

Given the initial value problem:
y'=6√(t+y), y(0)=1
Use Euler's method with step size h = 0.1 to estimate:
y(0.1) =
y(0.2) =

Use Euler's Method with step size 0.12 to approximate y (0.48)
for the solution of the initial value problem
y ′ = x + y, and y (0)= 1.2
What is y (0.48)? (Keep four decimal places.)

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 − 3x, y(4) = 0.y1 = y2 = y3 = y4 =

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