Question

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)

Answer #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...

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!

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.

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?

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)

For the initial value problem, Use Euler’s method with a step
size of h=0.25 to find approximate solution at x = 1

carry out n=4 steps of Euler's method with h=0.5 for the
following initial value problem:
y'=y-x, y(0)=2

1) Basic Euler’s Method:
y'+xysin/y+1 y(0)=1
a) What is the initial condition?
b) What order is this differential equation?
c) Is this an autonomous differential equation?
d) Is this a separable differential equation?
e) Find the general solution to the given differential equation,
by hand. You will not be able to completely solve for y(x) – that’s
ok. Write out all your work and attach it to your Questions
tab.
f) Using the initial condition, solve the initial value problem...

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.

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