Question

Use Euler's method to approximate *y*(1.2), where
*y*(*x*) is the solution of the initial-value
problem

x^{2}y'' − 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 *y*_{2}. (Round
your answers to four decimal places.)

y(1.2) | ≈ | (Euler approximation) | |

y(1.2) | = | (exact value) |

Answer #1

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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 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 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 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 ≈ y(0.5),
y2 ≈ y(1), y3 ≈
y(1.5), and y4 ≈ y(2) of the
solution of the initial-value problem
y′ = 1 + 2x − 2y,
y(0)=1.
y1 =
y2 =
y3 =
y4 =

Use Euler's Method to find the approximate value at x=0.5 with
h=0.1 given y' = y (6 - xy) and y(0) = 1.4.

Use Euler's method with step size 0.1 to estimate y(0.5), where
y(x) is the solution of the initial-value problem
y'=3x+y^2, y(0)=−1
y(0.5)=

Apply Euler's method twice to approximate the solution of the
equation y'=y-x-1, y(0)=1 at x=0.5. Use h=0.1.
a.
y(0.5)=1.089
b.
y(0.5)=0.579
c.
y(0.5)=1.534
d.
y(0.5)=0.889

Problem 6. Use Euler’s Method to approximate
the particular solution of this initial value problem (IVP):
dydx=√y+x satisfying the initial condition y(0)=1 on the
interval [0,0.4] with h = 0.1.
Round ?? to 4 decimal
places.

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