1. Find the general solution to y" - y = 0. 2. Take y" -2xy' + 4y = 0. (a) Show that y = 1-2r2 is a solution. (b) Use reduction of order to find a second linearly independent solution. (c) Write down the general solution. 3. Find the solution of y" - 17y' + 30y= 0 with y(0) = 1, y'(0) = −11. 4. Find the general solution to y" - 12y' + 36y= 0.
1. Find the general solution to y" - y = 0. 2. Take y" -2xy' + 4y = 0. (a) Show that y = 1-2r2 is a solution. (b) Use reduction of order to find a second linearly independent solution. (c) Write down the general solution. 3. Find the solution of y" - 17y' + 30y= 0 with y(0) = 1, y'(0) = −11. 4. Find the general solution to y" - 12y' + 36y= 0.
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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Transcribed Image Text:1. Find the general solution to y" - y = 0.
2. Take y" -2xy' + 4y = 0.
(a) Show that y = 1-2r2 is a solution.
(b) Use reduction of order to find a second linearly independent solution.
(c) Write down the general solution.
3. Find the solution of y" - 17y' + 30y= 0 with y(0) = 1, y'(0) = −11.
4. Find the general solution to y" - 12y' + 36y= 0.
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