Question

Consider the initial value problem 4u'' − u' + 2u = 0, u(0) = 5, u'(0)...

Consider the initial value problem 4u'' − u' + 2u = 0, u(0) = 5, u'(0) = 0. (a) Find the solution u(t) of this problem. u(t) = (b) For t > 0, find the first time at which |u(t)| = 10. (A computer algebra system is recommended. Round your answer to four decimal places.) t = Show My Work (Optional)

Homework Answers

Answer #1

I have solved the problem. You can do the 2nd one, you just need a graph plotter to find the value of t.

Hope you like it. Thanks for asking question.

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' + 5 4 y = 1 − t 5 ,    y(0)...
Consider the initial value problem y' + 5 4 y = 1 − t 5 ,    y(0) = y0. Find the value of y0 for which the solution touches, but does not cross, the t-axis. (A computer algebra system is recommended. Round your answer to three decimal places.) y0 =
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 following initial/boundary value problem: ∂u(t,x)/∂t = ∂^2u(t,x)/∂x^2 for t>0, 0<x<π, u(t,0)=u(t,π)=0 for t>0, u(0,x)=sin^2x...
Solve the following initial/boundary value problem: ∂u(t,x)/∂t = ∂^2u(t,x)/∂x^2 for t>0, 0<x<π, u(t,0)=u(t,π)=0 for t>0, u(0,x)=sin^2x for 0≤x≤ π. if you like, you can use/cite the solution of Fourier sine series of sin^2(x) on [0,pi] = 1/4-(1/4)cos(2x) please show all steps and work clearly so I can follow your logic and learn to solve similar ones myself.
1-Consider the following. 36y'' − y = 0, y(−4) = 1,   y'(−4) = −1 Find the...
1-Consider the following. 36y'' − y = 0, y(−4) = 1,   y'(−4) = −1 Find the solution of the given initial value problem. y(t) = ? 2- Consider the vibrating system described by the initial value problem. (A computer algebra system is recommended.) u'' + u = 9 cos ωt, u(0) = 5, u'(0) = 4 3-A spring is stretched 6 in. by a mass that weighs 8 lb. The mass is attached to a dashpot mechanism that has a...
6.                  Consider the initial value problem                   &
6.                  Consider the initial value problem                                            y'’ + 2y’ + 2y = δ(t − π);           y(0) = 0, y’(0) = 1. a.    Find the solution to the initial value problem. b.    Sketch a plot of the solution for t ∈ [0,3π]. c.    Describe the behavior of the solution. How is this system damped?
find the solution of the initial value-boundry vaule problem 8uxx=ut 0<x<8 t>=0 u(0,t)=0 u(8,t) = 4...
find the solution of the initial value-boundry vaule problem 8uxx=ut 0<x<8 t>=0 u(0,t)=0 u(8,t) = 4 u(x,0) = x
Consider the following. (A computer algebra system is recommended.) y' = 3x/(y+x^2y') (a) Find the solution...
Consider the following. (A computer algebra system is recommended.) y' = 3x/(y+x^2y') (a) Find the solution of the given initial value problem in explicit form. y' = 3x/(y+x^2y') y(0)=-6 question asks for answer in terms of y(x)= (b) Plot the graph of the solution.
4. a) solve the ff: Initial Value Problem: Eqtn : 2ut + XUx =0 U(X,0) =...
4. a) solve the ff: Initial Value Problem: Eqtn : 2ut + XUx =0 U(X,0) = f(X) b) Assuming f is C1,verify that u(x,t) =   f (xe^ -t/2 ) is a solution. 5) a) Solve the Initial Value problem: Eqtn : 2ut + XUx =0   U(X,0) = -X^2 +2X, ON THE DOMAIN 0 < x< 2 , t>2 b ) DRAW THE GRAPHS OF THE SOL. U(X,ti) as a function of X, FOR ti= 0, 0.1, 0.5, 1.0 c) HOW DO...
Consider the initial value problem 2y′′+11y′+5y=aδ(t−1), y(0)=y′(0)=0 , where δ denotes the impulse function. Suppose that...
Consider the initial value problem 2y′′+11y′+5y=aδ(t−1), y(0)=y′(0)=0 , where δ denotes the impulse function. Suppose that the solution of this initial value problem satisfies y(3)=(e^9−1)/e^10. Find the value of a.
Determine the solution of the following initial boundary-value problem Uxx=4Utt 0<x<Pi t>0 U(x,0)=sinx 0<=x<Pi Ut(x,0)=x 0<=x<Pi...
Determine the solution of the following initial boundary-value problem 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