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37. x²y" - 6xy' +12y = 0; x³, xª, (0, ∞) 20

37. x²y" - 6xy' +12y = 0; x³, xª, (0, ∞) 20

Advanced Engineering Mathematics
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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Can someone help me solve these problems 37 and 41
In Problems 33-40 verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. Form the general solution. 33. y" - y' - 12y = 0; e-3x, e4x, (-∞, ∞) 34. y" - 4y = 0; cosh 2x, sinh 2x, (-∞, ∞) 35. y" - 2y' + 5y = 0; 36. 4y" - 4y' + y = 0; 37. x²y" - 6xy' +12y = e* cos 2x, e* sin 2x, (-∞, ∞) ex/2, xex/2, (-∞, ∞) 0; x³, x¹, (0, ∞) 38. x²y" + xy' + y = 0; cos (In x), sin (In x), (0, ∞) 39. x³y" + 6x²y" + 4xy' - 4y = 0; x, x-², x-² ln x, (0, ∞) 40. y(4) + y″ = 0; 1, x, cos x, sin x, (−∞, ∞) In Problems 41-44 verify that the given two-parameter family of functions is the general solution of the nonhomogeneous differential equation on the indicated interval. 41. y" - 7y' + 10y = 24e* y = C₁e²x + c₂e³x + 6e*, (-∞, ∞)
Transcribed Image Text:In Problems 33-40 verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. Form the general solution. 33. y" - y' - 12y = 0; e-3x, e4x, (-∞, ∞) 34. y" - 4y = 0; cosh 2x, sinh 2x, (-∞, ∞) 35. y" - 2y' + 5y = 0; 36. 4y" - 4y' + y = 0; 37. x²y" - 6xy' +12y = e* cos 2x, e* sin 2x, (-∞, ∞) ex/2, xex/2, (-∞, ∞) 0; x³, x¹, (0, ∞) 38. x²y" + xy' + y = 0; cos (In x), sin (In x), (0, ∞) 39. x³y" + 6x²y" + 4xy' - 4y = 0; x, x-², x-² ln x, (0, ∞) 40. y(4) + y″ = 0; 1, x, cos x, sin x, (−∞, ∞) In Problems 41-44 verify that the given two-parameter family of functions is the general solution of the nonhomogeneous differential equation on the indicated interval. 41. y" - 7y' + 10y = 24e* y = C₁e²x + c₂e³x + 6e*, (-∞, ∞)
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