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In Problems 13–32 use variation of parameters to solve the given nonhomogeneous system.
28.
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Chapter 8 Solutions
First Course in Differential Equations (Instructor's)
- 29. Find a general solution to the following higher-order equations. (a) y-y"+y' + 3y = 0 (b) y" + 2y" + 5y' - 26y = 0 (c) ply 12. !!arrow_forward1. The Lotka-Volterra or predator-prey equations dU = aU – UV, dt (1) AP = eyUV – BV. dt (2) have two fixed points (U., V.) = (0,0), (U., V.) = (- :). The trivial fixed point (0,0) is unstable since the prey population grows exponentially if it is initially small. Investigate the stability of the second fixed point (U..V.) = 6:27 PM 3/3/2021 近arrow_forward2) 3 3 dr+du+ +y=t dr subject to x = 1 and y = 0 at t = 0arrow_forward
- 3. 2хydx - (3xу + 2y?)dy %3D0 o (x - 2y)*(2x +y) = c (х — у)"(х + у) %3 с (х + 2y) (2х- у)* %3 с (x – 2y)* = c(2x + y)arrow_forward1. Consider the accidental death model illustrated below. Let μ Alive 0 Dead-Accident Dead-Other Causes 2 10-5 and μ 7.4 x 10-5 and c = 1.05. Let = max (5,7). Calculate: (i) TP 00 (ii) po (iii)+p 01 A+ Bc for all x where A = 5 x 10-4, B =arrow_forward3. Suppose ay" + by' + cy = 0 with y(0) = d and y'(0) = k has a general solution y 4e2 - What are the constants a, b, c, d, and k ?arrow_forward
- Problem #1: Solve the following initial value problem. y = -2y₁ - y2 y = бу1 — 7уг y₁(0) = 5, y₂(0) = 3. Enter the functions y₁(x) and y2(x) (in that order) into the answer box below, separated with a comma. Do not include 'y₁(x) =' or 'y₂(x) =' in your answer. Problem #1: Enter your answer as a symbolic function of x, as in these examples Just Save Problem #1 Your Answer: Your Mark: Submit Problem #1 for Grading Attempt #1 Attempt #2 Attempt #3arrow_forward8.3 I only need number 14 pleasearrow_forwardProblem 13.3.5: Suppose heat is lost from the lateral surface of a thin rod of length L into a surrounding medium at temperature zero. If the linear law of heat transfer applies, then the heat equation takes on the form azu ди k hu 0 0 ´əx² at' where h is a constant. Find the temperature u(x, t) if the initial temperature is f (x) throughout and the ends x = 0 and x = L are insulated. See figure below. insulated 0° insulated 0° heat transfer from lateral surface of the rodarrow_forward
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