Question

Consider the initial value problem y''−y'+14y= 0, y(0) = 2, y'(0) =b, determine the value of...

Consider the initial value problem y''−y'+14y= 0, y(0) = 2, y'(0) =b,

determine the value of b that separates solutions that approach ∞ from those that approach −∞ as t→∞.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider the initial value problem: y' - (7/2)y = 7t + 2e^t Initial condition: y(0) =...
Consider the initial value problem: y' - (7/2)y = 7t + 2e^t Initial condition: y(0) = y0 a) Find the value of y0 that separates solutions that grow positively as t → ∞ from those that grow negatively. (A computer algebra system is recommended. Round your answer to three decimal places.) b) How does the solution that corresponds to this critical value of y0 behave as t → ∞? Will the corresponding solution increase without bound, decrease without bound, converge...
Solve the given initial-value problem. y''' + 14y'' + 49y' = 0, y(0) = 0, y'(0)...
Solve the given initial-value problem. y''' + 14y'' + 49y' = 0, y(0) = 0, y'(0) = 1, y''(0) = −5
Consider the initial value problem dy dx = 1−2x 2y , y(0) = − √2 (a)...
Consider the initial value problem dy dx = 1−2x 2y , y(0) = − √2 (a) (6 points) Find the explicit solution to the initial value problem. (b) (3 points) Determine the interval in which the solution is defined.
Consider the initial value problem given below. y' = (x+y+1)2 , y(0)= -1 The solution to...
Consider the initial value problem given below. y' = (x+y+1)2 , y(0)= -1 The solution to this initial value problem crosses the x-axis at a point in the interval [0, 1.4]. By experimenting with the improved Euler's method subroutine, determine this point to two decimal points.
Consider the initial value problem dy/dx= 6xy2 y(0)=1 a) Solve the initial value problem explicitly b)...
Consider the initial value problem dy/dx= 6xy2 y(0)=1 a) Solve the initial value problem explicitly b) Use eulers method with change in x = 0.25 to estimate y(1) for the initial value problem c) Use your exact solution in (a) and your approximate answer in (b) to compute the error in your approximation of y(1)
2. Solve the initial-value problem: y′′′ + 4y′ = t, y(0) = y′(0) = 0, y′′(0)...
2. Solve the initial-value problem: y′′′ + 4y′ = t, y(0) = y′(0) = 0, y′′(0) = 1.
Solve the initial value problem: y′′ − y = t + sint , y(0) = 2...
Solve the initial value problem: y′′ − y = t + sint , y(0) = 2 , y′(0) = 3.
Consider the following initial value problem. y′ + 5y  = { 0 t  ≤  2 10...
Consider the following initial value problem. y′ + 5y  = { 0 t  ≤  2 10 2  ≤  t  <  7 0 7  ≤  t  <  ∞ y(0)  =  5 (a) Find the Laplace transform of the right hand side of the above differential equation. (b) Let y(t) denote the solution to the above differential equation, and let Y((s) denote the Laplace transform of y(t). Find Y(s). (c) By taking the inverse Laplace transform of your answer to (b), the...
consider the initial value problem x"+16x=16u(t)-16u(t-2), x(0)=1, x'(0)=0 solve this initival value problem, and, for t>2...
consider the initial value problem x"+16x=16u(t)-16u(t-2), x(0)=1, x'(0)=0 solve this initival value problem, and, for t>2 determine the amplitude and period of the motion
Consider the initial value problem, ay''+by'+cy=0, y(0)=d, y'(0)=f where a,b,c,d and f are constants which one...
Consider the initial value problem, ay''+by'+cy=0, y(0)=d, y'(0)=f where a,b,c,d and f are constants which one of the following could be a solution to the initial value problem? Give breif exlpanation to why the correct answer can be a solution, and why the others can not possibly satisfy the equation. a. sin(t)+e^t b. cost+e^tsint c. cost+1 d. e^tcost