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) =
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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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,