Question

Consider the boundary value problem y''(t) + y(t) = f(t) , y(0) = 0 and y(π/2) = 0.

Find the solution to the boundary value problem

Answer #1

Find the solution of the given initial value problem: y " + y =
f(t); y(0) = 6, y' (0) = 3 where f(t) = 1, 0 ≤ t < π 2 0, π 2 ≤
t < ∞

A nontrivial solution of the boundary value problem y′′ + 9y =
0; y′(0) = 0, y′(π) = 0 is:

Solve the initial value problem
2(sin(t)dydt+cos(t)y)=cos(t)sin^3(t)
for 0<t<π0<t<π and y(π/2)=13.y(π/2)=13.
Put the problem in standard form.
Then find the integrating factor, ρ(t)=
and finally find y(t)=

Solve the given boundary-value problem.
y'' − 2y' + 2y = 2x − 2,
y(0) = 0, y(π) = π

Find the solution for the initial value problem.
(sint)y′ +(cost)y=t, y(π/2)=2

3) (A theoretical problem) Find the exact solution of the
two-point boundary-value problem x''=f(t), x(0)=x(1)=0

MATLAB CODE REQUIRED
Consider the problem of estimating y(0.5) for the boundary-value
problem
y''+ y' = y + 2, y(0) = 0, y'(1) = 2. Find the solution using 2
approaches:
(b) Use finite difference with n =
10.Please provide Matlab code. What is y(0.5) value with
Matlab?
(c) Using bvp4c. Please provide Matlab
code. What is y(0.5) value with Matlab?

Use the Laplace transform to solve the given initial-value
problem. y'' + y = f(t), y(0) = 0, y'(0) = 1, where f(t) = 0, 0 ≤ t
< π 5, π ≤ t < 2π 0, t ≥ 2π

obtain the green's function for the boundary value problem y''+y
= f(x), y(0)=y(1)=0

Given: The following boundary value problem:
y"+ lamda*y = 0;
0 < x < 2; y(0) =
0; y’(2) = 0
Find corresponding eigenvalues, (lamda)n
and normalized eigenfunctions yn
Expand the function f(x) = x, in terms of the eigen functions
obtained in (i)

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