Let y (t) be the solution of the initial value problemy"-4y +5y =e-2ty (0)17and y(0) =17%3DWhat is the asymptotic behavior of the solution y (t) as t goes to oo ?O A)0EThe solution osoillates and does not reach a limit

To find The asymptotic behaviours as t tends to infinity.

Let y (t) be the solution of the initial value problem y"-4y +5y =e-2t 1 y (0) and y(0) = 17 %3D 17 What is the asymptotic behavior of the solution y (t) as t goes to oo ? O A)0 E The solution osoillates and does not reach a limit

Let y (t) be the solution of the initial value problem y"-4y +5y =e-2t 1 y (0) and y(0) = 17 %3D 17 What is the asymptotic behavior of the solution y (t) as t goes to oo ? O A)0 E The solution osoillates and does not reach a limit

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: 2 What is the solution of the initial – value problem d²y =X O with y(0) = 1 dx? and y'(0) = -2 ? у…

Q: Find the solution of the initial value problem: y' (2x - 17)e, y(0) = In(72) = (a) Evaluate y(-1)…

Q: Suppose the equation y" – 4y' – 5y =f (x) has y = 3x³ as a solution. (a) Find f(x). (b) What is the…

Q: e y" (t) + 2y' (t) + y (t) = h (t) ; y (0) = 0, y' (0) = (t+ 1) for0 4

Q: Let y(x) be a continous solution of the initial value problem = Owhere f(x) = {1, 0 1} then find the…

Q: y=3 is an equilibrium solution for the d.e. y'-y=3 Select one: True O False

A: We have to check

Q: Find the steady periodic solution Xsp (t) = C cos (ot-a) of the given equation mx'' + cx' + kx =…

Q: Show that x(t) = e^t is a solution of tx′′ − (t + 1)x′ + x = 0 for t > 0.and solve the initial…

A: We need to show that x(t) = et is a solution of tx′′ − (t + 1)x′ + x = 0 for t > 0. Note: If x(t)…

Q: where y(0) = Find the matched asymptotic approximation to the solution of the problem ey" - y³ =…

A: To find the matched asymptotic approximation to the solution of the given problem, we will consider…

Q: If y (1-y)(2- y). then y 2 is O asymptotically stable O unstable O semi-stable O not an equilibrium…

A: The objective is to find the best suitable answer for : If y'=1-y2-y5 then y=2

Q: dyex Example// Solve = ex-Y dx Solution/ dy dy + Y = ex >> dx + p(x)y = Q(x) dx p(x) = 1 & Q(x) = ex…

A: Step 1: Step 2: Step 3: Step 4:

Q: a) Solve the initial value problem y + y = e", y(0) = 1, %3D where r E R.

A: y'+y=ex, y(0)=1y'+P(x)y=Q(x)Here,P(x)=1Q(x)=exIntegrating factorμ(x)=e∫P(x)dx =e∫1dx =ex

Q: y'1=4y1+8y2+2cost-16sint y'2=6y1+2y2+cost-14sint and y1 (0)=15 and y2 (0)=13 find y1 (t) and…

Q: Let y(t) be the solution of the IVP y = 2y- 3, y(1) = 2 then lim y(t) = Select one:

Q: Solve the initial value problem y" + 12y' + 37y = 0, y(0) = 1, y'(0) = 0 O y = 6e-6'cost + e-6f sint…

Q: dy dt = (y² - 16) (1 - y)² = 2. (a) Find the long term solution for initial value y(0) (b) If y…

A: Given differential equation:To find the long-term solution, we need to analyze the behavior of the…

Q: 2. (CV-3) Consider the initial value problem: y'(0) = -1, in which f(t) is a piecewise-continuous…

A: Given : y''+5y'-24y=ft , y0=3 , y'0=-1 To Find : Solution of initial value problem .

Q: Solve the initial value problem (2+a?)y" + ly = 0, y(0) = 0, y'(0) = 4 %3D If the solution is y = =…

Q: Find f by solving the initial-value problem. f'(x) = 9x² + 6x – 9; f(2) = 5 - f(x) %3D

A: Given, f'x = 9x2+6x-9 f2 = 5 We have to find fx

Q: Write the differential equation and then determine whether you have overdamped,critically damped,or…

A: Introduction: The differential equation of motion of an unforced damped harmonic oscillation is…

Q: -1 GTiven A=( 2-니 3 ) and ()A find A -3 H possible. It not state youre Teasoniong

A: Given: A=−132−4find:A5−6=?−34A=?

Q: 4. Consider the DE 3y' = (y – 1)(1 – 2y). (a) Which of the following is an explicit solution of the…

A: As per the company policy i can answer only first three subpart. More than that, leads me towards…

Q: (t) = C cos (@t-a) of the given equation mx'' + cx' + kx = F(t) with periodic forcing function F(t)…

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Let y (t) be the solution of the initial value problem
y"-4y +5y =e-2t
y (0)
17
and y(0) =
17
%3D
What is the asymptotic behavior of the solution y (t) as t goes to oo ?
O A)0
EThe solution osoillates and does not reach a limit

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Question 3 (Reduction of Order). Consider (t + 1)y" – (t+ 2)y' + y = 0 for t > -1. (b) second, linearly independent solution y2(t). Use the method of reduction of order to find a
1. (х + 2у)dx — Зуdy%3D0 x* – 6x²y² + 8xy³ – 3y* = c 3x* – 8x²y² + 6xy³ – y* = c o x* + 3x*y? – 4xy³ + 3y* = c o x* + 3x*y? – 6xy = c - 2. y'dx + (xy - 2x*)dy = 0 o x*y? = c(y+ – x²) o r²y* = c(y? – x²) o x*y? = c(y? +x²) o x*y? = c(y* +x²)
Theorem A. (Picard's theorem.) Let f (x, y) and of/dy be continuous functions of x and y on a closed rectangle R with sides parallel to the axes (Figure 105). If (xo, Yo) is any interior point of R, then there exists a number h>0 with the property that the initial value problem y' =f (x, y), y(x) = Yo (1) has one and only one solution y=y(x) on the interval |x – xo|
Please solve & show steps...
(2) For what value of c does y = cx + have a relative minimum at x = 2? ? (A) // (B) (C) 0 (D) 2 38
Solve initial value problem (engineering math) y" + 4y = f(t) y(0) = 2 y' (0)=0 with f(t) = 0 for 0 3
Let y (t) be the solution of the initial value problem y"- 4y +5y = e-2t y (0) = 17 2 and y(0) = -7 What is the asymptotic behavior of the solution y (t) as t goes to oo ? O A O O B )00 O D- EI The soution osoilatas and toes not reath a m
Sketch a graph of each of the following functions that captures the limiting behaviour as t → 0 and t → -00 and the oscillatory nature of the solution (include quasiperiod), if it has any. (a) y(t) = 16e*/2 – 12e*/3 (b) y(t) = ¿e=t + }e-3t (с) у (t) — —1 —е-3t
(2) For what value of c does y = cx + have a relative minimum at x = 2? ? (A) (B) (C) 0 (D) 2
Let y (z) be the solution of the initial value problem y(4) – y/" + 2y' + 2y = 0 y (0) = a, y (0) = B, y" (0) = 1, and y" (0) = -1 What are the values of a and B if lim y (r) = 0? O AI a =1 and B-1 O a =0 and B = -1 a = 1 and 3= -1 a = -1 and 3=0 and 3=1
method of reduction
7. A scientist found that the amount Q(t) of a substance present at time t 20 satisfies the equation: 40"(t) + 4Q'(t) + Q(t) = 0 (a) Verify Q(t) = A(1+t) e-0.5t satisfies the equation for A> 0 (b) If Q(0) = 10mg, find the maximum value of Q(t) and the time at which it occurs What happens to the amount of Q(t) as t→∞? (c)