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8. xy" - xy + y = 0 y₁(x) = x

8. xy" - xy + y = 0 y₁(x) = x

Calculus For The Life Sciences
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 1CR
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can you please explain how to get the result for number 8 please. I am so lost

PROBLEMS: Section 3.3 For Problems 1-10, a differential equation and one solution are given. Use d'Alembert's reduction of order method to find a second linearly independent solution. What is the general solution of the differential equation? Differential equation 1. y" - y = 0 2. y" + y =0 3. " - 4y' + 4y = 0 4. " +y' = 0 5. " + y = 0 6. xy" - 2(x + 1)y' + 4y = 0 7." - 6y = 0 8. x²y" - xy + y = 0 9. (²+1)y" - 2xy' + 2y = 0 Solution Y₁(x) = et y₁(x) = sin x y₁(x) = ²x y₁(x) = 1 y₁(x) = 1 y₁(x) = ²x y₁(x) = x³ y₁(x) = x y₁(x) = x
Transcribed Image Text:PROBLEMS: Section 3.3 For Problems 1-10, a differential equation and one solution are given. Use d'Alembert's reduction of order method to find a second linearly independent solution. What is the general solution of the differential equation? Differential equation 1. y" - y = 0 2. y" + y =0 3. " - 4y' + 4y = 0 4. " +y' = 0 5. " + y = 0 6. xy" - 2(x + 1)y' + 4y = 0 7." - 6y = 0 8. x²y" - xy + y = 0 9. (²+1)y" - 2xy' + 2y = 0 Solution Y₁(x) = et y₁(x) = sin x y₁(x) = ²x y₁(x) = 1 y₁(x) = 1 y₁(x) = ²x y₁(x) = x³ y₁(x) = x y₁(x) = x
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