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2) Find the homogeneous linear ODE for which the given functions are Basis. -2x -2x , N, = Xe ", y3 = e²x cos 3x, y₁ = e²x sin 3x a) y₁ = e

2) Find the homogeneous linear ODE for which the given functions are Basis. -2x -2x , N, = Xe ", y3 = e²x cos 3x, y₁ = e²x sin 3x a) y₁ = e

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1) Find the general solution for the following ODE using Undetermined Coefficients Method. State which rule you are using. If the initial condition is given find the particular solution. a) (D² − 4D+31)y=e* - 4.5x b) y" +4y=-12sin 2x; y(0) = 2, y'(0) = 5 c) (D² -4D³ +4D²)y=48x; y(0)=1, y'(0)=2, y"(0)=0, y" (0)=0 d) (D³ +4D² +3D)y=3 2) Find the homogeneous -2.x a) y₁=e , Y₂ 2 = xe -2.x -2.x 9 linear ODE for which the given functions are Basis. Y3 = e²x cos 3x, y₁ = e²x sin 3x -2x b) y₁=e сOS лx, y₂ = e c) y₁ = x, y₂ = x², d) Y3 = -2.x sin лx, y3 = xe COS IC YA = xe sin zx -2x = x² In/x| y₁= x², y₂ = xcos 2ln | x, y3 = xsin 2 ln | x | e) y₁=e³x cos x, y₂ = e³x sinx, y₂ = cos x, y4 = sin x f) y₁=1, y₂ = xsin 2 lnx, y3 = xcos 2 ln|x|
Transcribed Image Text:1) Find the general solution for the following ODE using Undetermined Coefficients Method. State which rule you are using. If the initial condition is given find the particular solution. a) (D² − 4D+31)y=e* - 4.5x b) y" +4y=-12sin 2x; y(0) = 2, y'(0) = 5 c) (D² -4D³ +4D²)y=48x; y(0)=1, y'(0)=2, y"(0)=0, y" (0)=0 d) (D³ +4D² +3D)y=3 2) Find the homogeneous -2.x a) y₁=e , Y₂ 2 = xe -2.x -2.x 9 linear ODE for which the given functions are Basis. Y3 = e²x cos 3x, y₁ = e²x sin 3x -2x b) y₁=e сOS лx, y₂ = e c) y₁ = x, y₂ = x², d) Y3 = -2.x sin лx, y3 = xe COS IC YA = xe sin zx -2x = x² In/x| y₁= x², y₂ = xcos 2ln | x, y3 = xsin 2 ln | x | e) y₁=e³x cos x, y₂ = e³x sinx, y₂ = cos x, y4 = sin x f) y₁=1, y₂ = xsin 2 lnx, y3 = xcos 2 ln|x|
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