Question

How would one solve this?

Use the RK4 method to obtain a four decimal approximation of the indicated value.

Use h = 0.1 ,

y ' = x + y^2 ,

y(0) = 0,

find y(0.5).

Thank you for your help and time!

Answer #1

Use Euler’s Method to obtain a five-decimal approximation of the
indicated value. Carry out the recursion by hand, using h = 0.1 and
then using h = 0.05.
y′ = -y + x + 1, y(0) = 1. Find
y(1)

Use Euler's method to obtain a four-decimal approximation of the
indicated value. Carry out the recursion of (3) in Section 2.6
yn + 1 = yn + hf(xn,
yn) (3)
by hand, first using h = 0.1 and then using h = 0.05.
y' = 2x − 3y + 1, y(1) = 7; y(1.2)

Use the RK4 method with h=0.1 to obtain a 4-decimal
approximation of the indicated value: y' = x2 +
y2, y(0) = 1; y(1.3)
If you could make a table with the values up to 1.3 that is what
I am looking for. I already solved the first line (F1, F2, F3, and
F4). I am just unsure where to find a code/program to create a
table. All I had to do was write out the work by hand for...

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

Use Newton's method with the specified initial approximation x1
to find x3, the third approximation to the root of the given
equation. (Round your answer to four decimal places.) 2x^3 − 3x^2 +
2 = 0, x1 = −1

Use Newton's method with the specified initial approximation
x1 to find x3, the third
approximation to the root of the given equation.
x3 + 5x − 2 =
0, x1 = 2
Step 1
If
f(x) =
x3 + 5x − 2,
then
f'(x) = _____ x^2 + _____
2- Use Newton's method to find all roots of the
equation correct to six decimal places. (Enter your answers as a
comma-separated list.)
x4 = 5 + x
.

Use Eulerʹs method with the specified step size to approximate
the solution. 18. Use Eulerʹs method with h = 0.1 to estimate
y(0.5) if yʹ = 4x - y and y(0) = 8. Round your answer to five
decimal places. Show your work

Use Euler’s method with h = π/4 to solve y’ = y cos(x) ,
y(0) = 1 on the interval [0, π] to find y(π)

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