Solve q3 5 7 and 9 8:21 AMA 93%Differential Equa..168CHAPTER 4HIGHER-ORDER DIFFERENTIAL EQUATIONSEXERCISES 4.7Answers to selected odd-numbered problems begin on pag-In Problems 1–18 solve the given differential equation.35. х*у" — Зху'+ 13у %3D 4 + 3х1. х^у" — 2у %3D02. 4x?y" + у 3 036. ху" — Зх?у" + бху' — бу —D 3 + In x3-3. ху" + у' — 04. ху" — Зу' %3D 0In Problems 37 and 38 solve the given initial-valueon the interval (-∞, 0).5. x²y" + xy' + 4y = 06. x²y" + 5xy' + 3y = 07. х2у" — Зху - 2у 3D 08. x?y" + 3xy' – 4y = 037. 4x²y" + y = 0, y(-1) = 2, y'(-1) = 49. 25x²y" + 25xy' + y = 010. 4x2у" + 4ху' — у %3D 038. ху" — 4ху' + бу %3D 0, у(-2) %3 8, у'(-2) —311. x²y" + 5xy' + 4y = 012. ху" + 8ху'+ бу %3D 0Discussion Problems13. Зx2у" + 6ху' + у %3D 014. x²y" – 7xy' + 41y = 0-39. How would you use the method of this section15. х3у" — бу %3D 016. х3у" + ху' — у %3D 0(x + 2)²y" + (x + 2)y' + y = 0?17. xy(4) + 6y" = 018. х4у (4) + 6х3у" + 9х?у" + Зху' + у%3D0Carry out your ideas. State an interval over wlsolution is defined.In Problems 19–24 solve the given differential equation byvariation of parameters.40. Can a Cauchy-Euler differential equation oforder with real coefficients be found if it is kno2 and 1 – i are roots of its auxiliary equation.out your ideas.19. ху" — 4у' %3D х420. 2.x?y" + 5xy' + y = x² – x41. The initial-conditions y(0) = yo, y'(0) = yı aeach of the following differential equations:21. х?у" — ху'+у%3D 2x22. x²y" – 2xy' + 2y = x*e*x²y" = 0,23. x?y" + xy' – y = In x24. ху" + ху' — у %3Dx + 1x?y" – 2xy' + 2y = 0,In Problems 25–30 solve the given initial-value problem.Use a graphing utility to graph the solution curve.x²y" – 4xy' + 6y = 0.For what values of yo and yı does each initi25. х?у" + Зху%3D 0, у(1) 3D 0, у' (1) 3D 4problem have a solution?26. ху" — 5ху'+ 8y %3D 0, у(2) %3D 32, у' (2) %3D 042. What are the x-intercepts of the solution curvein Figure 4.7.1? How many x-intercepts are tlif x 027. x²y" + xy' + y = 0, y(1) = 1, y'(1) = 228. xу" — Зху' + 4y%3D 0, у(1) — 5, у'(1) 3 329. ху" + у' %3D х, у(1) %3D 1, у'(1) %3D —Computer Lab AssignmentsIn Problems 43–46 solve the given differential equausing a CAS to find the (approximate) roots of the aequation.30. x²y" – 5xy' + 8y = 8rº, y(})= 0, y'(}) = 0In Problems 31–36 use the substitution x = e' to transformthe given Cauchy-Euler equation to a differential equationwith constant coefficients. Solve the original equation bysolving the new equation using the procedures inSections 4.3–4.5.43. 2.x°y" – 10.98x²y" + 8.5xy' + 1.3y = 044. x³y" + 4x²y" + 5xy' – 9y = 045. х*у0) + 6х3у" + 3x?у" — Зху'+ 4y %3D031. x?y" + 9xy' – 20y = 046. x*y(4) – 6x³y" + 33x?y"169y =32. х?у"9ху' + 25у %3 047. Solve x³y" - x²y" -I variaparameters. Use a CAthe auxiliary equation(10) of Section 4.6.33. х?у" + 10ху' + 8у %3D х?utingnants g34. x?у" — 4ху' + бу 3DIn x2

Question

Solve q3 5 7 and 9 8:21 AMA 93%Differential Equa..168CHAPTER 4HIGHER-ORDER DIFFERENTIAL EQUATIONSEXERCISES 4.7Answers to selected odd-numbered problems begin on pag-In Problems 1–18 solve the given differential equation.35. х*у&#34; — Зху'+ 13у %3D 4 + 3х1. х^у&#34; — 2у %3D02. 4x?y&#34; + у 3 036. ху&#34; — Зх?у&#34; + бху' — бу —D 3 + In x3-3. ху&#34; + у' — 04. ху&#34; — Зу' %3D 0In Problems 37 and 38 solve the given initial-valueon the interval (-∞, 0).5. x²y&#34; + xy' + 4y = 06. x²y&#34; + 5xy' + 3y = 07. х2у&#34; — Зху - 2у 3D 08. x?y&#34; + 3xy' – 4y = 037. 4x²y&#34; + y = 0, y(-1) = 2, y'(-1) = 49. 25x²y&#34; + 25xy' + y = 010. 4x2у&#34; + 4ху' — у %3D 038. ху&#34; — 4ху' + бу %3D 0, у(-2) %3 8, у'(-2) —311. x²y&#34; + 5xy' + 4y = 012. ху&#34; + 8ху'+ бу %3D 0Discussion Problems13. Зx2у&#34; + 6ху' + у %3D 014. x²y&#34; – 7xy' + 41y = 0-39. How would you use the method of this section15. х3у&#34; — бу %3D 016. х3у&#34; + ху' — у %3D 0(x + 2)²y&#34; + (x + 2)y' + y = 0?17. xy(4) + 6y&#34; = 018. х4у (4) + 6х3у&#34; + 9х?у&#34; + Зху' + у%3D0Carry out your ideas. State an interval over wlsolution is defined.In Problems 19–24 solve the given differential equation byvariation of parameters.40. Can a Cauchy-Euler differential equation oforder with real coefficients be found if it is kno2 and 1 – i are roots of its auxiliary equation.out your ideas.19. ху&#34; — 4у' %3D х420. 2.x?y&#34; + 5xy' + y = x² – x41. The initial-conditions y(0) = yo, y'(0) = yı aeach of the following differential equations:21. х?у&#34; — ху'+у%3D 2x22. x²y&#34; – 2xy' + 2y = x*e*x²y&#34; = 0,23. x?y&#34; + xy' – y = In x24. ху&#34; + ху' — у %3Dx + 1x?y&#34; – 2xy' + 2y = 0,In Problems 25–30 solve the given initial-value problem.Use a graphing utility to graph the solution curve.x²y&#34; – 4xy' + 6y = 0.For what values of yo and yı does each initi25. х?у&#34; + Зху%3D 0, у(1) 3D 0, у' (1) 3D 4problem have a solution?26. ху&#34; — 5ху'+ 8y %3D 0, у(2) %3D 32, у' (2) %3D 042. What are the x-intercepts of the solution curvein Figure 4.7.1? How many x-intercepts are tlif > x > 027. x²y&#34; + xy' + y = 0, y(1) = 1, y'(1) = 228. xу&#34; — Зху' + 4y%3D 0, у(1) — 5, у'(1) 3 329. ху&#34; + у' %3D х, у(1) %3D 1, у'(1) %3D —Computer Lab AssignmentsIn Problems 43–46 solve the given differential equausing a CAS to find the (approximate) roots of the aequation.30. x²y&#34; – 5xy' + 8y = 8rº, y(})= 0, y'(}) = 0In Problems 31–36 use the substitution x = e' to transformthe given Cauchy-Euler equation to a differential equationwith constant coefficients. Solve the original equation bysolving the new equation using the procedures inSections 4.3–4.5.43. 2.x°y&#34; – 10.98x²y&#34; + 8.5xy' + 1.3y = 044. x³y&#34; + 4x²y&#34; + 5xy' – 9y = 045. х*у0) + 6х3у&#34; + 3x?у&#34; — Зху'+ 4y %3D031. x?y&#34; + 9xy' – 20y = 046. x*y(4) – 6x³y&#34; + 33x?y&#34;169y =32. х?у&#34;9ху' + 25у %3 047. Solve x³y&#34; - x²y&#34; -I variaparameters. Use a CAthe auxiliary equation(10) of Section 4.6.33. х?у&#34; + 10ху' + 8у %3D х?utingnants g34. x?у&#34; — 4ху' + бу 3DIn x2

Accepted Answer

Cauchy Euler differential equation

3. xy" + y' = 0