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If y₁ is a known nonvanishing solution of y" + p(t)y' + g(t)y = 0, then a second solution y₂ satisfies W(V1, V2) Y₁² where W(Y₁, Y₂) is the Wronskian of y₁ and y₂. To determine y2, use Abel's formula, W(y₁, Y₂) (t) = C. e-p(t) dt, where C is a certain constant that depends on y₁ and y₂, but not on t. Use the method above to find a second independent solution of the given equation. (x - 1)y" - xy + y = 0, x> 1; ₁(x) = ex Y₂(x) = 2 X

If y₁ is a known nonvanishing solution of y" + p(t)y' + g(t)y = 0, then a second solution y₂ satisfies W(V1, V2) Y₁² where W(Y₁, Y₂) is the Wronskian of y₁ and y₂. To determine y2, use Abel's formula, W(y₁, Y₂) (t) = C. e-p(t) dt, where C is a certain constant that depends on y₁ and y₂, but not on t. Use the method above to find a second independent solution of the given equation. (x - 1)y" - xy + y = 0, x> 1; ₁(x) = ex Y₂(x) = 2 X

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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If y₁ is a known nonvanishing solution of y" + p(t)y' + g(t)y = 0, then a second solution y₂ satisfies W(V1, V2) Y₁² where W(Y₁, Y₂) is the Wronskian of y₁ and y₂. To determine y2, use Abel's formula, W(y₁, Y₂) (t) = C. e-p(t) dt, where C is a certain constant that depends on y₁ and y₂, but not on t. Use the method above to find a second independent solution of the given equation. (x - 1)y" - xy + y = 0, x> 1; ₁(x) = ex Y₂(x) = 2 X
Transcribed Image Text:If y₁ is a known nonvanishing solution of y" + p(t)y' + g(t)y = 0, then a second solution y₂ satisfies W(V1, V2) Y₁² where W(Y₁, Y₂) is the Wronskian of y₁ and y₂. To determine y2, use Abel's formula, W(y₁, Y₂) (t) = C. e-p(t) dt, where C is a certain constant that depends on y₁ and y₂, but not on t. Use the method above to find a second independent solution of the given equation. (x - 1)y" - xy + y = 0, x> 1; ₁(x) = ex Y₂(x) = 2 X
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