A third-order homogeneous linear equation and three linearly independent solutions are given below. Find a particular solution satisfying the given initial conditions. y(3) +9y' = 0; y(0) = 3, y'(0) = -4, y''(0) = 1; Y₁ = 1, y₂ = cos (3x), y3 = sin (3x) The particular solution is y(x) =

A third-order homogeneous linear equation and three linearly independent solutions are given below. Find a particular solution satisfying the given initial conditions. y(3) +9y' = 0; y(0) = 3, y'(0) = -4, y''(0) = 1; Y₁ = 1, y₂ = cos (3x), y3 = sin (3x) The particular solution is y(x) =

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.1: Solutions Of Elementary And Separable Differential Equations

Problem 15E: Find the general solution for each differential equation. Verify that each solution satisfies the...

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Question

A third-order homogeneous linear equation and three linearly independent solutions are given below. Find a particular solution satisfying the given initial conditions.
y(3) +9y' = 0; y(0) = 3, y'(0) = -4, y''(0) = 1;
Y₁ = 1, y₂ = cos (3x), y3 = sin (3x)
The particular solution is y(x) =

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