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In this exercise you will solve the initial value problem (1) Let C₁ and C₂ be arbitrary constants. The general solution the related homogeneous differential equation y" - 22y' + 121y = 0 is the function yn(x) = C₁ y₁(x) + C₂ Y₂ (x) = C₁ +C₂ e-11x y" 22y' + 121y = 1+x²¹ y(0) = -10, y'(0) = 6. NOTE: The order in which you enter the answers is important; that is, C₁f(x) + C₂g(x) # C₁9(x) + C₂f(x). e-11x 1+x2 is of the form y(x) = y₁(x) u₁(x) + y₂ (x) u₂(x) where u₁(x) = (2) The particular solution y(x) to the differential equation y" + 22y' + 121y = and u₂(x) = y = (3) The most general solution to the non-homogeneous differential equation y" - 22y' + 121y = e-11x 1+x2 + dt + dt

In this exercise you will solve the initial value problem (1) Let C₁ and C₂ be arbitrary constants. The general solution the related homogeneous differential equation y" - 22y' + 121y = 0 is the function yn(x) = C₁ y₁(x) + C₂ Y₂ (x) = C₁ +C₂ e-11x y" 22y' + 121y = 1+x²¹ y(0) = -10, y'(0) = 6. NOTE: The order in which you enter the answers is important; that is, C₁f(x) + C₂g(x) # C₁9(x) + C₂f(x). e-11x 1+x2 is of the form y(x) = y₁(x) u₁(x) + y₂ (x) u₂(x) where u₁(x) = (2) The particular solution y(x) to the differential equation y" + 22y' + 121y = and u₂(x) = y = (3) The most general solution to the non-homogeneous differential equation y" - 22y' + 121y = e-11x 1+x2 + dt + dt

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.2: Trigonometric Equations
Problem 27E
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In this exercise you will solve the initial value problem y" 22y' + 121y = -11x e 1 + x²¹ y(0) = − 10, y'(0) = 6. (1) Let C₁ and C₂ be arbitrary constants. The general solution to the related homogeneous differential equation y" - 22y' + 121y = 0 is the function yn(x) = C₁ y₁ (x) + C₂ y₂(x) = C₁ +C₂ y = NOTE: The order in which you enter the answers is important; that is, C₁f(x) + C₂g(x) ‡ C₁9(x) + C₂f(x). (2) The particular solution y(x) to the differential equation y" + 22y' + 121y = is of the form y(x) = y₁(x) u₁(x) + y₂ (x) u₂(x) where u₁(x) 11x 1+x² and u₂(x) = (3) The most general solution to the non-homogeneous differential equation y" - 22y' + 121y = e-11x 1+x2 dt + is dt
Transcribed Image Text:In this exercise you will solve the initial value problem y" 22y' + 121y = -11x e 1 + x²¹ y(0) = − 10, y'(0) = 6. (1) Let C₁ and C₂ be arbitrary constants. The general solution to the related homogeneous differential equation y" - 22y' + 121y = 0 is the function yn(x) = C₁ y₁ (x) + C₂ y₂(x) = C₁ +C₂ y = NOTE: The order in which you enter the answers is important; that is, C₁f(x) + C₂g(x) ‡ C₁9(x) + C₂f(x). (2) The particular solution y(x) to the differential equation y" + 22y' + 121y = is of the form y(x) = y₁(x) u₁(x) + y₂ (x) u₂(x) where u₁(x) 11x 1+x² and u₂(x) = (3) The most general solution to the non-homogeneous differential equation y" - 22y' + 121y = e-11x 1+x2 dt + is dt
Find a particular solution to Ур y" - 2y' + y = 11et t² + 1 .
Transcribed Image Text:Find a particular solution to Ур y" - 2y' + y = 11et t² + 1 .
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In this exercise you will solve the initial value problem y" 22y' + 121y = -11x e 1 + x²¹ y(0) = − 10, y'(0) = 6. (1) Let C₁ and C₂ be arbitrary constants. The general solution to the related homogeneous differential equation y" - 22y' + 121y = 0 is the function yn(x) = C₁ y₁ (x) + C₂ y₂(x) = C₁ +C₂ y = NOTE: The order in which you enter the answers is important; that is, C₁f(x) + C₂g(x) ‡ C₁9(x) + C₂f(x). (2) The particular solution y(x) to the differential equation y" + 22y' + 121y = is of the form y(x) = y₁(x) u₁(x) + y₂ (x) u₂(x) where u₁(x) 11x 1+x² and u₂(x) = (3) The most general solution to the non-homogeneous differential equation y" - 22y' + 121y = e-11x 1+x2 dt + is dt
Transcribed Image Text:In this exercise you will solve the initial value problem y" 22y' + 121y = -11x e 1 + x²¹ y(0) = − 10, y'(0) = 6. (1) Let C₁ and C₂ be arbitrary constants. The general solution to the related homogeneous differential equation y" - 22y' + 121y = 0 is the function yn(x) = C₁ y₁ (x) + C₂ y₂(x) = C₁ +C₂ y = NOTE: The order in which you enter the answers is important; that is, C₁f(x) + C₂g(x) ‡ C₁9(x) + C₂f(x). (2) The particular solution y(x) to the differential equation y" + 22y' + 121y = is of the form y(x) = y₁(x) u₁(x) + y₂ (x) u₂(x) where u₁(x) 11x 1+x² and u₂(x) = (3) The most general solution to the non-homogeneous differential equation y" - 22y' + 121y = e-11x 1+x2 dt + is dt
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