Write the general solution of the ODEs by finding two power series solutions about the ordinary point x = 0. Write out the first three nonzero terms in each series. a. y" + x²y = 0

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.2: Sequences, Series And Summation Notation
Problem 51E
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Write the general solution of the ODEs by finding two power series solutions about the
ordinary point x = 0. Write out the first three nonzero terms in each series.
a. y" + x²2y = 0
Transcribed Image Text:Write the general solution of the ODEs by finding two power series solutions about the ordinary point x = 0. Write out the first three nonzero terms in each series. a. y" + x²2y = 0
1
a. y(x) = C₁ (1 − 1⁄2 x+ + (3)(4) (7) (8) x² + ...) + C₂ (x −12/1² x ² + ₁
¯ (4)(5)(®)(9) x² + ...)
20
Transcribed Image Text:1 a. y(x) = C₁ (1 − 1⁄2 x+ + (3)(4) (7) (8) x² + ...) + C₂ (x −12/1² x ² + ₁ ¯ (4)(5)(®)(9) x² + ...) 20
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