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Consider the following differential equation (1-12)y" +2ty' = 0 Given that y₁=1 is a non-trivial solution, find a second linearly independent solution using reduction of order. Use the Wronskian to verify that y, and y₂ are linearly independent over the interval (1,00). Write the general solution.

Consider the following differential equation (1-12)y" +2ty' = 0 Given that y₁=1 is a non-trivial solution, find a second linearly independent solution using reduction of order. Use the Wronskian to verify that y, and y₂ are linearly independent over the interval (1,00). Write the general solution.

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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Existence and unique theorem. Differential equations. 

Consider the following differential equation (1-t2)y" +2ty' = 0 Given that y₁=1 is a non-trivial solution, find a second linearly independent solution using reduction of order. Use the Wronskian to verify that y, and y₂ are linearly independent over the interval (1,00). Write the general solution.
Transcribed Image Text:Consider the following differential equation (1-t2)y" +2ty' = 0 Given that y₁=1 is a non-trivial solution, find a second linearly independent solution using reduction of order. Use the Wronskian to verify that y, and y₂ are linearly independent over the interval (1,00). Write the general solution.
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