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11. y' y + e, y (x + c)e, y(0) = %3D

11. y' y + e, y (x + c)e, y(0) = %3D

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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7. y' cosh 5.13x 8. y" = -0.27 9-15 VERIFICATION. INITIAL VALUE PROBLEM (IVP) 19 (a) Verify that y is a solution of the ODE. (b) Determine from y the particular solution of the IVP. (c) Graph the solution of the IVP. 9. y' + 4y 1.4, -4.c + 0.35, y(0) = 2 y(0) 7 y(0) = y = ce 10. v -2.52 V = ce 11. y' =y + e, y (x+ c)e", 12. yy' = 4x, y - 4x = c (y > 0), y(1) = 4 1 13. y' = y - y2, y = y(0) = 0.25 1 + ce 14. y' tan x = 2y - 8, y c sin2 x + 4, yTT) = 0 20. E 15. Find two constant solutions of the ODE in Prob. 13 by inspection. pr Fi 16. Singular solution. An ODE may sometimes have an additional solution that cannot be obtained from the inf to general solution and is then called a singular solution. The ODE y2 - xy' +y = 0 is of this kind. Show Vo that by differentiation and substitution that it has the with aeneral solutionv= 2and the singular solution F3 F4 F5 F6 F7 F8 F9 23 24
Transcribed Image Text:7. y' cosh 5.13x 8. y" = -0.27 9-15 VERIFICATION. INITIAL VALUE PROBLEM (IVP) 19 (a) Verify that y is a solution of the ODE. (b) Determine from y the particular solution of the IVP. (c) Graph the solution of the IVP. 9. y' + 4y 1.4, -4.c + 0.35, y(0) = 2 y(0) 7 y(0) = y = ce 10. v -2.52 V = ce 11. y' =y + e, y (x+ c)e", 12. yy' = 4x, y - 4x = c (y > 0), y(1) = 4 1 13. y' = y - y2, y = y(0) = 0.25 1 + ce 14. y' tan x = 2y - 8, y c sin2 x + 4, yTT) = 0 20. E 15. Find two constant solutions of the ODE in Prob. 13 by inspection. pr Fi 16. Singular solution. An ODE may sometimes have an additional solution that cannot be obtained from the inf to general solution and is then called a singular solution. The ODE y2 - xy' +y = 0 is of this kind. Show Vo that by differentiation and substitution that it has the with aeneral solutionv= 2and the singular solution F3 F4 F5 F6 F7 F8 F9 23 24
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