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2. In a. and b. (below), show that y₁() satisfies the given differential equation. Then, use the reduction of order method to find the second linearly independent solution. Finally, write the general solution of the DE. a. 2t²y" + ty - 3y = 0, b. 4x²y" + y = 0, y₁ (t) = t-¹. x² ln x, y₁ (x): = x2 x > 0.

2. In a. and b. (below), show that y₁() satisfies the given differential equation. Then, use the reduction of order method to find the second linearly independent solution. Finally, write the general solution of the DE. a. 2t²y" + ty - 3y = 0, b. 4x²y" + y = 0, y₁ (t) = t-¹. x² ln x, y₁ (x): = x2 x > 0.

Calculus: Early Transcendentals
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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2. In a. and b. (below), show that y₁() satisfies the given differential equation. Then, use the reduction of order method to find the second linearly independent solution. Finally, write the general solution of the DE. a. 2t²y" +ty' − 3y = 0, b. 4x²y" + y = 0, y₁ (t) = t-¹. 3₁(x) = x² ln x. x > 0.
Transcribed Image Text:2. In a. and b. (below), show that y₁() satisfies the given differential equation. Then, use the reduction of order method to find the second linearly independent solution. Finally, write the general solution of the DE. a. 2t²y" +ty' − 3y = 0, b. 4x²y" + y = 0, y₁ (t) = t-¹. 3₁(x) = x² ln x. x > 0.
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