Question

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

Answer #1

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

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

Find the solution to the boundary value problem:
d2y/dt2−4dy/dt+3y=0, y(0)=7,y(1)=8
y=

Solve the given initial-value problem.
y''' + 6y'' +
9y' = 0, y(0) = 0,
y'(0) = 1, y''(0) = −6

Solve the given initial-value problem. y’’ + 9y = 0, y(0) = 6,
y’(0) = −3

Find the Laplace transform Y(s)=L{y} of the solution of the
given initial value problem.
y′′+9y={t, 0≤t<1 1, 1≤t<∞, y(0)=3, y′(0)=4
Enclose numerators and denominators in parentheses. For example,
(a−b)/(1+n).
Y(s)=

For what values of a (if any) does the boundary value
problem
x'' + ax' = 0, x(0) = 0, x(π) = 0
have nontrivial (i.e. nonzero) solutions
Hint: In order to solve, divide the problem into three
cases
1. If a > 0. In this case let a = b^2. 2. If a < 0. In this
case let a = −b^2. 3. If a = 0.

For what values of a
(if any) does the boundary value problem
x'' + ax = 0, x(0) = 0, x(π) = 0
have nontrivial (i.e. nonzero) solutions
Hint: In order to
solve, divide the problem into three cases
1. If a > 0. In this case let a = b^2. 2. If a < 0. In this
case let a = −b^2. 3. If a = 0.

Give the solution to the given boundary value problem y''+y=18x
y(0)=0 y(1)+y'(1)=0
answer:
3x- (6sin(sqrt6) x)/(sin(sqrt of 6)x +(sqrt 6) cos(sqrt6)

Solve the initial value problem: 9y′′−18y′+15y=09y″−18y′+15y=0,
y(π/3)=2y(π/3)=2, y′(π/3)=1.y′(π/3)=1.Give your answer as y=...
y=... . Use xx as the independent variable.

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