Use the method above to find a second independent solution of the equation ty" - y' + 4t³y = 0, t > 0; y₁(t) = sin(t²).

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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If y₁ is a known nonvanishing
a second solution y2 satisfies
the Wronskian of y₁ and y2. To determine y2, use Abel's formula,
W (y₁, y2) (t) = c· e¯Sp(t)dt, where c is a certain constant that depends
and Y2, but not on t.
on yı
solution of y" + p(t)y' + q(t)y = 0, then
W (y₁, 92) where W (y₁, y2) is
(12)' _ W (152, 92),
Y2
y²
Use the method above to find a second independent solution of the
equation ty" - y' + 4t³y = 0, t > 0; y₁(t) = sin(t²).
y₂(t) =
=
Transcribed Image Text:If y₁ is a known nonvanishing a second solution y2 satisfies the Wronskian of y₁ and y2. To determine y2, use Abel's formula, W (y₁, y2) (t) = c· e¯Sp(t)dt, where c is a certain constant that depends and Y2, but not on t. on yı solution of y" + p(t)y' + q(t)y = 0, then W (y₁, 92) where W (y₁, y2) is (12)' _ W (152, 92), Y2 y² Use the method above to find a second independent solution of the equation ty" - y' + 4t³y = 0, t > 0; y₁(t) = sin(t²). y₂(t) = =
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