Question

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.)

Answer #1

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 0.5 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 =

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 − 4x,
y(4) = 0.
y1 =
y2 =
y3 =
y4 =

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

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)=

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 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 − 2x, y(4) = 2.
y1= ?
y2 = ?
y3 = ?
y4 = ?

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(3) = 2.
y1 =
y2 =
y3 =
y4 =

Use Euler's method with step size 0.4 to estimate y ( 0.8 ) ,
where y ( x ) is the solution of the initial-value problem y' = 4x
+ y^2 ,
y ( 0 ) = 0 .
y ( 0.8 ) =_____________________

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.

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