Solve the initial value problem: y''-2y'+y=0, y(0)=2, y'(0)=1 . A) Write its characteristic equation. B) Write...

Question

Question

Solve the initial value problem: y''-2y'+y=0, y(0)=2, y'(0)=1 .

A) Write its characteristic equation.

B) Write a fundamental set of solutions of the homogenous equation.

C) Prove that your solutions from B) are independent.

D) Find the solution satisfying initial conditions.

Answer 1

Answer #1

Griven initial value problemis y_2y! + y = 0 0. with Y 602=2,.yilo) (A) Here, the characteristic equt of is m2 • 2ml =) (m-1

Answer 2

Similar Homework Help Questions

Consider the differential equation y" + 8y' + 15 y=0. (a) Find r1 r2, roots of...

Consider the differential equation y" + 8y' + 15 y=0. (a) Find r1 r2, roots of the characteristic polynomial of the equation above. = 11, 12 M (b) Find a set of real-valued fundamental solutions to the differential equation above. yı(t) M y2(t) M (C) Find the solution y of the the differential equation above that satisfies the initial conditions y(0) = 4, y(0) = -3. g(t) = M (10 points) Solve the initial value problem y" - 54' +...
Consider the differential equation y" – 7y + 12 y = 0. (a) Find r1, 72,...

Consider the differential equation y" – 7y + 12 y = 0. (a) Find r1, 72, roots of the characteristic polynomial of the equation above. 11,2 M (b) Find a set of real-valued fundamental solutions to the differential equation above. yı(t) M y2(t) M (C) Find the solution y of the the differential equation above that satisfies the initial conditions y(0) = -4, y'(0) = 1. g(t) = M Consider the differential equation y" – 64 +9y=0. (a) Find r1...
Let Lyl = y + 2y + y (a) Solve the initial value problem L[y]=0 y(0)=1...

Let Lyl = y + 2y + y (a) Solve the initial value problem L[y]=0 y(0)=1 (y'0)=1 (b) Use the method of undetermined coefficients to find a particular solution to the equation L[y] =2e-4

y"+ 2y' + y = 0, y(0) = 1 and y(1) = 3 Solve the initial-value...

y"+ 2y' + y = 0, y(0) = 1 and y(1) = 3 Solve the initial-value differential equation y"+ 4y' + 4y = 0 subject to the initial conditions y(0) = 2 and y' = 1 Mathematical Physics 2 H.W.4 J."+y'-6y=0 y"+ 4y' + 4y = 0 y"+y=0 Subject to the initial conditions (0) = 2 and y'(0) = 1 y"- y = 0 Subject to the initial conditions y(0) = 2 and y'(0) = 1 y"+y'-12y = 0 Subject...
(4) Consider the IVP 9y" + 6y' +2y = 0, y(37) = 0, y/(3x) = }:...

(4) Consider the IVP 9y" + 6y' +2y = 0, y(37) = 0, y/(3x) = }: a) Determine the roots of the characteristic equation. b) Obtain the general solution as linear combination of real-valued solutions. c) Impose the initial conditions and solve the initial value problem.
2. Solve the initial value problem using method of Laplace transforms: y" + 2y' + 2y...

2. Solve the initial value problem using method of Laplace transforms: y" + 2y' + 2y = 3e1 satisfying y(0) 0 y'(0) =-1

21. Solve the initial value problem y" - y-2y= 0, y(0) = a , y (...

21. Solve the initial value problem y" - y-2y= 0, y(0) = a , y ( 0) the solution approaches zero as t 0o. 2. Then find a so that
4. Consider the following initial value problem: y(0) = e. (a) Solve the IVP using the...

4. Consider the following initial value problem: y(0) = e. (a) Solve the IVP using the integrating factor method. (b) What is the largest interval on which its solution is guaranteed to uniquely exist? (c) The equation is also separable. Solve it again as a separable equation. Find the particular solution of this IVP. Does your answer agree with that of part (a)? 5 Find the general solution of the differential equation. Do not solve explicitly for y. 6,/Solve explicitly...
Problem 2. (a) Solve the initial value problem I y' + 2y = g(t), 1 y(0)...

Problem 2. (a) Solve the initial value problem I y' + 2y = g(t), 1 y(0) = 0, where where | 1 if t < 1, g(t) = { 10 if t > 1 (t) = { for all t. Is this solution unique for all time? Is it unique for any time? Does this contradict the existence and uniqueness theorem? Explain. (b) If the initial condition y(0) = 0 were replaced with y(1) = 0, would there necessarily be...

2) (10) Find the integrating factor and solve the initial value problem -2xy + y(1) Find...

2) (10) Find the integrating factor and solve the initial value problem -2xy + y(1) Find an interval of solution w of cooling, the rate at which the temperature of an object isproportional to the difference between the temperature 3) (10) In Newton's law of cooling, the rate at whic changes over time is proportional to the of the object (t) and the temperature of the surrounding medium For the following problem set up the initial value problem, then solve...