A third-order homogeneous linear equation and three linearly independent solutions are given. Find a particular solution satisfying the given initial conditions. x³y(3)-3x²y" +6xy' -6y=0; y(1) = 6, y'(1) = 18, y''(1) = 22; V₁ = X, Y₂ = X, Y3 = X
A third-order homogeneous linear equation and three linearly independent solutions are given. Find a particular solution satisfying the given initial conditions. x³y(3)-3x²y" +6xy' -6y=0; y(1) = 6, y'(1) = 18, y''(1) = 22; V₁ = X, Y₂ = X, Y3 = 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.CR: Chapter 11 Review
Problem 12CR
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![A third-order homogeneous linear equation and three linearly
independent solutions are given. Find a particular solution satisfying
the given initial conditions.
x³y(3) - 3x²y' +6xy' - 6y=0; y(1) = 6, y'(1) = 18, y''(1) = 22;
3
Y₁ = X₁ Y₂ = x², y₂ = x³
X, Y2
X, Y3
A general solution is y(x) = C₁x + C₂x² + 3x³
The particular solution is y(x) =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F55ae2c3d-db8a-4868-8838-b7d4cd87465a%2Fa3d0b6cf-f06c-4335-921c-8a78cc5d7f27%2Flij5yzl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A third-order homogeneous linear equation and three linearly
independent solutions are given. Find a particular solution satisfying
the given initial conditions.
x³y(3) - 3x²y' +6xy' - 6y=0; y(1) = 6, y'(1) = 18, y''(1) = 22;
3
Y₁ = X₁ Y₂ = x², y₂ = x³
X, Y2
X, Y3
A general solution is y(x) = C₁x + C₂x² + 3x³
The particular solution is y(x) =
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