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"+ xy' + 2y = 0 Obtain the recurrence relation. as as+2 s +1 as as+2 s +2 а, as+2 = s + 2 as Oas+2 ° s +1

"+ xy' + 2y = 0 Obtain the recurrence relation. as as+2 s +1 as as+2 s +2 а, as+2 = s + 2 as Oas+2 ° s +1

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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Solve the given ODE using the power series method. y'' + xy' + 2y = 0 4. Obtain the recurrence relation. as as+2 = s +1 as Oas+2 s + 2 as Oas+2 - s + 2 as Oas+2 s +1 5. Determine the general solution. Use up to the 5th-degree term of the solution. 1 1 + 1 1 y = ao 1 + a1 x 3 15 --) = ao 1 + a1 ( x ... ... 1 1 x + 1 1 x* + + a1( x + 3 y = ao(1+ + ... ... 15 1 y = ao(1+x² +x* + ... + a1 ( x + 1 + -x° + ... 3 6. Solve for y at x = 2 given the boundary conditions x = 0, y = 1, and y' = 2. Use up to the 5th-degree term of the solution. Write your answer in three decimal places. Time remaining: 01:33 +
Transcribed Image Text:Solve the given ODE using the power series method. y'' + xy' + 2y = 0 4. Obtain the recurrence relation. as as+2 = s +1 as Oas+2 s + 2 as Oas+2 - s + 2 as Oas+2 s +1 5. Determine the general solution. Use up to the 5th-degree term of the solution. 1 1 + 1 1 y = ao 1 + a1 x 3 15 --) = ao 1 + a1 ( x ... ... 1 1 x + 1 1 x* + + a1( x + 3 y = ao(1+ + ... ... 15 1 y = ao(1+x² +x* + ... + a1 ( x + 1 + -x° + ... 3 6. Solve for y at x = 2 given the boundary conditions x = 0, y = 1, and y' = 2. Use up to the 5th-degree term of the solution. Write your answer in three decimal places. Time remaining: 01:33 +
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