In: Advanced Math

Calculate the Euler method approximation to the solution of the initial value problem at the given x-values. Compare your results to the exact solution at these x-values.

y' = y+y^2; y(1) = -1, x = 1.2, 1.4, 1.6, 1.8

Use Eulers method to find approximate values of the solution of
the given initial value problem at T=0.5 with h=0.1.
12. y'=y(3-ty) y(0)=0.5

Use the method of Undetermined Coefficients to find the solution
of the initial value value problem:
y'' + 8y' + 20y = 9cos(2t) - 18e-4t, y(0) = 5. y'(0)
= 0

1) Find the solution of the given initial value problem and
describe the behavior of the solution as t → +∞
y" + 4y' + 3y = 0, y(0) = 2, y'(0) = −1.
2) Find a differential equation whose general solution is
Y=c1e2t + c2e-3t
3) Determine the longest interval in which the given initial
value problem is certain to have a unique twice-differentiable
solution. Do not attempt to find the solution t(t − 4)y" + 3ty' +
4y...

use the method of order two to approximate the solution to the
following initial value problem y'=e^(t-y),0<=t<=1, y(0)=1,
with h=0.5

Compute, by Euler’s method, an approximate solution to the
following initial value problem for h = 1/8 : y’ = t − y , y(0) = 2
; y(t) = 3e^(−t) + t − 1 . Find the maximum error over [0, 1]
interval.

In exercises 1–4, verify that the given formula is a solution to
the initial value problem.
2. Powers of t.
b) y ′ = t^3 , y(0) = 5: y(t) = (1/5)t^(4) + 5
3. Sines and cosines.
a) x′ = −y, y′ = x, x(0) = 1, y(0) = 0: x(t) = cost, y(t) =
sint

Determine the unique solution of the given initial value
problem that is valid in any interval not including the singular
point.
4x2
y’’ + 8xy’ + 17y =
0; y(1)
= 2, y’ (1) = 2(31/2 )− 1
please show all steps

Determine the solution of the following initial boundary-value
problem using the method of separation of Variables
Uxx=4Utt 0<x<Pi t>0
U(x,0)=sinx 0<=x<Pi
Ut(x,0)=x 0<=x<Pi
U(0,t)=0 t>=0
U(pi,t)=0 t>=0

Find the solution of the given initial value problem.
y(4) + 2y''' + y'' + 8y' − 12y = 12 sin t −
e−t; y(0) =
7, y'(0) = 0, y''(0)
= −1, y'''(0) = 2

solve the given initial value problem using the method of
Laplace transforms.
Y'' + Y = U(t-4pi) y(0) =1 y'(0) = 0

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