Need help for 34 please 3.5 ProblemsIn Problems 1 through 20, find a particular solution yp of thegiven equation. In all these problems, primes denote deriva-tives with respect to x.3. у" + 9у — sin 2x; y (0) — 1, у' (0) — 034. y" + y = cos x; y(0) = 1, y'(0) = –135. у" — 2у' + 2у %3D х + 1; у(0) — 3, у' (0) —D 036. y(4) – 4y" = x²; y(0) = y' (0) = 1, y"(0) = y(3) (0) =37. y(3) – 2y" + y' = 1 + xe*; y(0) = y'(0) = 0, y"(0) = 138. у" + 2y' + 2у %3 sin 3x; y (0) 3 2, у' (0) %3D 039. y(3) + y" = x +e¯*; y(0) = 1, y'(0) = 0, y"(0) = 140. y(4) – y = 5; y(0) = y'(0) = y"(0) = y(3) (0) = 041. Find a particular solution of the equation= -11. у" + 16у — еЗx3. у" — у' — бу — 2 sin 3x5. y" + y' + y = sin? x7. у" — 4у — sinh x9. y" + 2y' – 3y = 1 + xe*10. y" + 9y = 2 cos 3x + 3 sin 3x11. y(3) + 4y' = 3x – 113. у" + 2у' + 5у — е* sin x15. у(5) + 5у(4) — у %3D 172. у" — у' — 2у — Зх + 44. 4y" + 4y' + у %3D 3хе*6. 2y" + 4y' + 7y = x²8. y" – 4y = cosh 2xy(4) – y(3) – y" – y' – 2y = 8x5.12. y(3) + y' = 2 – sin x14. у(4) — 2у" + у %— хе*16. у" + 9у 3D 2х?езx + 542. Find the solution of the initial value problem consistingof the differential equation of Problem 41 and the initialconditions17. y" + y = sin x + x cos x18. y(4) – 5y" + 4y = e* – xe2x19. y(5) + 2y(3) +2y" = 3x?20. y(3) – y = e* +7y (0) = y'(0) = y"(0) = y(3) (0)= 0.- 143. (а) Writecos 3x + i sin 3x= e31x(cos x + i sinx)³In Problems 21 through 30, set up the appropriate form of aparticular solutioncoefficients.by Euler's formula, expand, and equate real and imag-inary parts to derive the identitiesУр»but do not determine the values of thecos x =cos x + cos 3x,21. у" — 2у + 2y — е* sin x22. y(5) – y(3) = e* +2x² – 523. у" + 4у %— 3x cos 2x24. у(3) — у" — 12y' — х — 2хе Зх25. y" + 3y' + 2y = x(e-* – e-2x)26. у" — бу' + 13у — хезx sin 2x27. y(4) + 5y" + 4y28. y(4) + 9y" = (x² + 1) sin 3x29. (D — 1)3 (D2 — 4)у %3 хе* + е2х +е-2х30. y(4) – 2y" + y = x² cos xsin' x =sin xi sin 3x.=(b) Use the result of part (a) to find a general solution ofy" + 4y = cos³ x.Use trigonometric identities to find general solutions of theequations in Problems 44 through 46.= sin x + cos 2x44. y" + y' + y = sin x sin 3x45. y" + 9y = sin* x46. у" + у — х cos3 xSolve the initial value problems in Problems 31 through 40.31. у" + 4y32. y" + 3y' + 2y = e*; y(0) = 0, y'(0) = 3In Problems 47 through 56, use the method of variation of pa-rameters to find a particular solution of the given differentialequation.= 2x; y(0) = 1, y'(0) = 2

Name: Need help for 34 please 3.5 ProblemsIn Problems 1 through 20, find a p
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Description: Need help for 34 please 3.5 ProblemsIn Problems 1 through 20, find a particular solution yp of thegiven equation. In all these problems, primes denote deriva-tives with respect to x.3. у" + 9у — sin 2x; y (0) — 1, у' (0) — 034. y" + y = cos x; y(0) =