In Problems 17 through 26, first verify that y(x) satisfies the 20. y' = x- y; y(x) = Ce +x-1, y(0) = 10 given differential equation. Then determine a value of the con- 21. y' + 3x2y 0; y(x) = Ce-x', y(0) =7 stant C so that y(x) satisfies the given initial condition. Use a 22. e y' = 1; y(x) In(x +C), y(0) 0 computer or graphing calculator (if desired) to sketch several typical solutions of the given differential equation, and high- light the one that satisfies the given initial condition. %3D dy (23. x+3y 2x5; y(x) = x Cx-3, y(2) = 1 %3D dx 24. xy'-3y x3; y(x) = x(C+In x), y(1) = 17 25. y' 3x2 (y2 + 1); y(x) = tan(x³ + C), y(0) 1 26. y' +y tanx cos.r; y(x) = (x+ C)cosxr, y(x) = 0 %3D 17. y'+y 0; y(x) = Ce-, y(0) = 2 18. y' = 2y; y(x) = Ce2x, y(0) = 3 19. y' = y + 1; y(x) = Ce-1, y (0) = 5 %3D %3! %3D %3D %3D %3D %3D %3D %3D
In Problems 17 through 26, first verify that y(x) satisfies the 20. y' = x- y; y(x) = Ce +x-1, y(0) = 10 given differential equation. Then determine a value of the con- 21. y' + 3x2y 0; y(x) = Ce-x', y(0) =7 stant C so that y(x) satisfies the given initial condition. Use a 22. e y' = 1; y(x) In(x +C), y(0) 0 computer or graphing calculator (if desired) to sketch several typical solutions of the given differential equation, and high- light the one that satisfies the given initial condition. %3D dy (23. x+3y 2x5; y(x) = x Cx-3, y(2) = 1 %3D dx 24. xy'-3y x3; y(x) = x(C+In x), y(1) = 17 25. y' 3x2 (y2 + 1); y(x) = tan(x³ + C), y(0) 1 26. y' +y tanx cos.r; y(x) = (x+ C)cosxr, y(x) = 0 %3D 17. y'+y 0; y(x) = Ce-, y(0) = 2 18. y' = 2y; y(x) = Ce2x, y(0) = 3 19. y' = y + 1; y(x) = Ce-1, y (0) = 5 %3D %3! %3D %3D %3D %3D %3D %3D %3D
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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Transcribed Image Text:NUMBER 23
In Problems 17 through 26, first verify that y(x) satisfies the 20. y' = x- y; y(x) = Ce +x-1, v(0) = 10
given differential equation. Then determine a value of the con- 21. y' + 3x2y 0; y(x) = Ce-, y(0) =7
stant C so that y(x) satisfies the given initial condition. Use a 22. e y' 1; y(x) = In(x + C), y(0) 0
computer or graphing calculator (if desired) to sketch several
typical solutions of the given differential equation, and high-
light the one that satisfies the given initial condition.
dy
(23.) x-
xp,
+ 3y = 2x5; y(x) = Cr-3, y(2) = 1
24. xy'-3y x3; y(x) = r(C +In x), y(1) = 17
25. y' = 3x2(y2 + 1); y(x) = tan(r3 +C), y(0) = 1
26. y'+y tan x cos.r; y(x) = (r+ C) cosx, y() = 0
17. y'+y 0; y(x) = Ce-, y(0) = 2
18. y' 2y; y(x) = Ce2x, y(0) = 3
19. y' = y + 1; y(x) = Ce-1, y (0) = 5
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