y' + 2y = 4 cos2x, y(1/4 pi) = 2

From,

Advanced Engineering Mathematics

byErwin Kreyszig

1.5 Problem 8

0.0 KBps X Page 9 0.0 KBps ZOOM + A few further population models will be discussed in the problem set. For some more details of population dynamics, see C. W. Clark, Mathematical Bioeconomics, New York, Wiley, 1976. Further important applications of linear ODEs follow in the next section. PROBLEM SET 1. (CAUTION!) Show that e-In * = 1/x (not -x) and 6. x2y' + 3xy = 1/x, y'(1) = -1 e-In(sec #) = cosx. 7. y' + ky = 2kex 2. (Integration constant) Give a reason why in (4) you 8. y' + 2y = 4 cos 2x, y(47) = 2 may choose the constant of integration in Jp dx to be 9. y' = 6(y - 2.5) tanh 1.5.x zero 10. y' + 4x2y = (4x2 - x)e- 2/2 3-17 GENERAL SOLUTION. INITIAL VALUE 11. y' + 2y sin 2x = 2ecos 2x, y(0) = 0 PROBLEMS 12. y' tan x = 2y - 8, y(T) = 0 Find the general solution. If an initial condition is given, find also the corresponding particular solution and graph or 13. y' + 4y cot 2x = 6 cos 2x, y(47) = 2 sketch it. (Show the details of your work.) 14. y' + y tan x = e-0.018 cos x, y(0) = 0 3. y' + 3.5y = 2.8 15. y' + y/x2 = 2xellz, y(1) = 13.86 4. y' = 4y + x 16. y' cos x + 3y = 1, y(47) = 3 5. y' + 1.25y = 5, >(0) = 6.6 17. xBy' + 3x2y = 5 sinh 10x