equation? 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, e¹x, (-∞, ∞) 34. y" - 4y = 0; cosh 2x, sinh 2x, (-∞, ∞) 35. y" - 2y' + 5y = 0; 36. 4y" - 4y' + y = 0; 37. x²y" - 6xy' +12y = 38. x²y" + xy' + y = 0; e cos 2x, e* sin 2x, (-∞0,00) ex/2, xex/², (-∞, ∞) 0; x³, x4, (0, ∞) cos (In x), sin (In x), (0, ∞) 39. x³y" + 6x²y" + 4xy' - 4y = 0; x, x2, x 2ln x, (0, ∞) 40. y(4) + y" = 0; 1, x, cos x, sin x, (-∞, ~)
equation? 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, e¹x, (-∞, ∞) 34. y" - 4y = 0; cosh 2x, sinh 2x, (-∞, ∞) 35. y" - 2y' + 5y = 0; 36. 4y" - 4y' + y = 0; 37. x²y" - 6xy' +12y = 38. x²y" + xy' + y = 0; e cos 2x, e* sin 2x, (-∞0,00) ex/2, xex/², (-∞, ∞) 0; x³, x4, (0, ∞) cos (In x), sin (In x), (0, ∞) 39. x³y" + 6x²y" + 4xy' - 4y = 0; x, x2, x 2ln x, (0, ∞) 40. y(4) + y" = 0; 1, x, cos x, sin x, (-∞, ~)
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 .33 and 35
Transcribed Image Text:equation?
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, e¹x, (-∞, ∞)
34. y" - 4y = 0; cosh 2x, sinh 2x, (-∞, ∞)
35. y" - 2y' + 5y = 0;
36. 4y" - 4y' + y = 0;
37. x²y" - 6xy' +12y =
38. x²y" + xy' + y = 0;
e cos 2x, e* sin 2x, (-∞0,00)
ex/2, xex/², (-∞, ∞)
0; x³, x4, (0, ∞)
cos (In x), sin (In x), (0, ∞)
39. x³y" + 6x²y" + 4xy' - 4y = 0; x, x2, x 21n x, (0, ∞)
40. y(4) + y" = 0; 1, x, cos x, sin x, (-∞, ~)
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