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4.1 x²y" (x) + 2xy' (x) - 3y(x) = 0 2²

4.1 x²y" (x) + 2xy' (x) - 3y(x) = 0 2²

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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Question 4 please sectio. 8.5
1 8.5 EXERCISES In Problems 1-10, use the substitution y = x' to find a gen- eral solution to the given equation for x>0. 1. x²y" (x) + 6xy' (x) + 6y(x) = 0 2. 2x²y" (x) + 13xy' (x) + 15y(x) = 0 3. x²y" (x) - xy' (x) + 17y(x) = 0 4.I x²y" (x) + 2xy' (x) − 3y(x) = 0 d'y 1 dy dx² x dx 7. x³y"" (x) + 4x²y" (x) + 10xy' (x) - 10y(x) = 0 8. x³y"(x) + 4x²y"(x) + xy' (x) = 0 9. x³y"" (x) + 3x²y" (x) + 5xy' (x) - 5y(x) = = 0 10. x³y" (x) +9x²y" (x) + 19xy' (x) + 8y(x) = 0 5. 2 W S 5 dy 13 x dx x² # 3 In Problems 11 and 12, use a substitution of the form y = (x-c)' to find a general solution to the given equation for x> c. 11. 2(x-3)²y" (x) +5(x-3)y'(x) - 2y(x) = 0 12. 4(x+2)3y"(x) +5y(x) = 0 80 E $ described in this section will lead to the de 4 - 888 R % 6. 5 d'y dx² T 6 F6 Y & 4 2 Y 7 x² U 8 In Pr 15. t 16. x y( 17. x y (1 18. Supp ar²_ is a s a, b, one g equati early in 19. Let L[ (a) She (b) Usi sect has
Transcribed Image Text:1 8.5 EXERCISES In Problems 1-10, use the substitution y = x' to find a gen- eral solution to the given equation for x>0. 1. x²y" (x) + 6xy' (x) + 6y(x) = 0 2. 2x²y" (x) + 13xy' (x) + 15y(x) = 0 3. x²y" (x) - xy' (x) + 17y(x) = 0 4.I x²y" (x) + 2xy' (x) − 3y(x) = 0 d'y 1 dy dx² x dx 7. x³y"" (x) + 4x²y" (x) + 10xy' (x) - 10y(x) = 0 8. x³y"(x) + 4x²y"(x) + xy' (x) = 0 9. x³y"" (x) + 3x²y" (x) + 5xy' (x) - 5y(x) = = 0 10. x³y" (x) +9x²y" (x) + 19xy' (x) + 8y(x) = 0 5. 2 W S 5 dy 13 x dx x² # 3 In Problems 11 and 12, use a substitution of the form y = (x-c)' to find a general solution to the given equation for x> c. 11. 2(x-3)²y" (x) +5(x-3)y'(x) - 2y(x) = 0 12. 4(x+2)3y"(x) +5y(x) = 0 80 E $ described in this section will lead to the de 4 - 888 R % 6. 5 d'y dx² T 6 F6 Y & 4 2 Y 7 x² U 8 In Pr 15. t 16. x y( 17. x y (1 18. Supp ar²_ is a s a, b, one g equati early in 19. Let L[ (a) She (b) Usi sect has
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