please help for # 16 and 19 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.1. y" + 16y3. у" — у' — 6у — 2 sin 3x5. y" + y' + y = sin?7. у" — 4у 3 sinh x9. y" + 2y' – 3y = 1+ xe*10. у" + 9у %3D 2 cos 3x + 3 sin 3x33. y" + 9y = sin 2x; y(0) = 1, y'(0) = 034. y" + y = cos x; y(0) = 1, y'(0) = –135. y" – 2y' + 2y = x + 1; y(0) = 3, y'(0) = 036. y(4) – 4y" = x²; y(0) = y'(0) = 1, y"(0) = y(3) (0) = -137. y(3) – 2y" + y' = 1 + xe*; y(0) = y'(0) = 0, y"(0) = 138. у" + 2y' + 2у39. 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 equation2. y" — у' — 2у — Зх + 44. 4y" + 4y' + y = 3xe*6. 2y" + 4y' + 7y = x²8. y" – 4y = cosh 2xe 3x,//sin 3x; y(0) = 2, y'(0) = 0,//-y(4) – y(3) – y" – y' – 2y = 8x°.11. у(3) + 4у' 3 3х — 113. y" + 2y' + 5y = e* sin x15. y(5) + 5y(4) – y = 1712. у (3)14. y(4) – 2y" + y = xe*16. y" + 9y = 2x²e3x + 5»(3)+ y' = 2 – sin x42. Find the solution of the initial value problem consistingof the differential equation of Problem 41 and the initialconditions17. у" + у 3D sin x + xcos x18. y(4) – 5y" + 4y = e* – xe2x19. y(5) + 2y(3) + 2y" = 3x² – 120. y(3) – y = e* +7y (0) = y'(0) = y"(0) = y(3) (0) = 0.-43. (а) WriteЗіхcos 3x +i sin 3x= (cos x +i sin x)3= e

Name: please help for # 16 and 19 3.5 ProblemsIn Problems 1 through 20, find
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Description: please help for # 16 and 19 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.1. y" + 16y3. у" — у' — 6у — 2 sin 3x5. y" + y' + y = sin?7. у"

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please help for # 16 and 19 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.1. y&#34; + 16y3. у&#34; — у' — 6у — 2 sin 3x5. y&#34; + y' + y = sin?7. у&#34; — 4у 3 sinh x9. y&#34; + 2y' – 3y = 1+ xe*10. у&#34; + 9у %3D 2 cos 3x + 3 sin 3x33. y&#34; + 9y = sin 2x; y(0) = 1, y'(0) = 034. y&#34; + y = cos x; y(0) = 1, y'(0) = –135. y&#34; – 2y' + 2y = x + 1; y(0) = 3, y'(0) = 036. y(4) – 4y&#34; = x²; y(0) = y'(0) = 1, y&#34;(0) = y(3) (0) = -137. y(3) – 2y&#34; + y' = 1 + xe*; y(0) = y'(0) = 0, y&#34;(0) = 138. у&#34; + 2y' + 2у39. y(3) + y&#34; = x +e-*; y(0) = 1, y'(0) = 0, y&#34;(0) = 140. y(4) – y = 5; y(0) = y'(0) = y&#34;(0) = y(3) (0) = 041. Find a particular solution of the equation2. y&#34; — у' — 2у — Зх + 44. 4y&#34; + 4y' + y = 3xe*6. 2y&#34; + 4y' + 7y = x²8. y&#34; – 4y = cosh 2xe 3x,//sin 3x; y(0) = 2, y'(0) = 0,//-y(4) – y(3) – y&#34; – y' – 2y = 8x°.11. у(3) + 4у' 3 3х — 113. y&#34; + 2y' + 5y = e* sin x15. y(5) + 5y(4) – y = 1712. у (3)14. y(4) – 2y&#34; + y = xe*16. y&#34; + 9y = 2x²e3x + 5»(3)+ y' = 2 – sin x42. Find the solution of the initial value problem consistingof the differential equation of Problem 41 and the initialconditions17. у&#34; + у 3D sin x + xcos x18. y(4) – 5y&#34; + 4y = e* – xe2x19. y(5) + 2y(3) + 2y&#34; = 3x² – 120. y(3) – y = e* +7y (0) = y'(0) = y&#34;(0) = y(3) (0) = 0.-43. (а) WriteЗіхcos 3x +i sin 3x= (cos x +i sin x)3= e

Accepted Answer

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16. y" + 9y = 2x²e3x + 5 %3D