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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 following differential equations by power series and also by an elementary method. Verify that the series solution is the power series expansion of your other solution. 1. "=-4y 2. y = xy + x 3. xy = xy + y 5. 7. y = 3x²y 9. y"+y = 4x sin x "-2y+y=0 4. y"+y=4 sin 3x 6. xy' - y = x² 8. xy" 3xy+3y=0 10. y=x+y-1 Solve the following differential equations by power series. II. y" − xảy' – xy = () 13. y + xy = 0 15. 17. y" 4xy +(4x² - 2)y=0 (x2+2x)" - 2(x + 1) + 2y = 0 12. y(x²+1)y = 0 14. "2y = 4x²x² 16. 18. " + xy + y = 0 (x²+1)-2xy + 2y = 0
Transcribed Image Text:Solve the following differential equations by power series and also by an elementary method. Verify that the series solution is the power series expansion of your other solution. 1. "=-4y 2. y = xy + x 3. xy = xy + y 5. 7. y = 3x²y 9. y"+y = 4x sin x "-2y+y=0 4. y"+y=4 sin 3x 6. xy' - y = x² 8. xy" 3xy+3y=0 10. y=x+y-1 Solve the following differential equations by power series. II. y" − xảy' – xy = () 13. y + xy = 0 15. 17. y" 4xy +(4x² - 2)y=0 (x2+2x)" - 2(x + 1) + 2y = 0 12. y(x²+1)y = 0 14. "2y = 4x²x² 16. 18. " + xy + y = 0 (x²+1)-2xy + 2y = 0
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