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Solve the 2nd-order homogeneous Cauchy-Euler equation ry" +23ry' +12ly = 0 The linearly independent solutions are 9/1 = 9x 9/2== and the general solution of the equation is y (z): where 1, and 2 are arbitrary constants. (Note: Let 1 and 2 be two solutions of the auxiliary (characteristic) equation. and 1/2 = x; (1) If m₁m2, write 9/11 < (i) If m₁m2, write 3/1 = and 3/2 = In (z) z; and (iii) If m₁ = a +bi, and m₂ = a-bi, write 9/1 = cos (bln (r)) and 3/2=2 sin (6 ln (z)).)

Solve the 2nd-order homogeneous Cauchy-Euler equation ry" +23ry' +12ly = 0 The linearly independent solutions are 9/1 = 9x 9/2== and the general solution of the equation is y (z): where 1, and 2 are arbitrary constants. (Note: Let 1 and 2 be two solutions of the auxiliary (characteristic) equation. and 1/2 = x; (1) If m₁m2, write 9/11 < (i) If m₁m2, write 3/1 = and 3/2 = In (z) z; and (iii) If m₁ = a +bi, and m₂ = a-bi, write 9/1 = cos (bln (r)) and 3/2=2 sin (6 ln (z)).)

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Solve the 2nd-order homogeneous Cauchy-Euler equation r²y + 23ry + 121y = 0 The linearly independent solutions are 3/2= and the general solution of the equation is y (r) = where ei, and are arbitrary constants. (Note: Let 1 and 2 be two solutions of the auxiliary (characteristic) equation. (1) If m1m2, write /1 and 1/2 = ""; ® and 2 In (r); and = (ii) If m1m2, write /1 = (iii) If m₁ = a +bi, and m₂ = a-bi, write 9/1 = cos (bln (r)) and 2 = sin (bln (z)).) symbolic formatting help
Transcribed Image Text:Solve the 2nd-order homogeneous Cauchy-Euler equation r²y + 23ry + 121y = 0 The linearly independent solutions are 3/2= and the general solution of the equation is y (r) = where ei, and are arbitrary constants. (Note: Let 1 and 2 be two solutions of the auxiliary (characteristic) equation. (1) If m1m2, write /1 and 1/2 = ""; ® and 2 In (r); and = (ii) If m1m2, write /1 = (iii) If m₁ = a +bi, and m₂ = a-bi, write 9/1 = cos (bln (r)) and 2 = sin (bln (z)).) symbolic formatting help
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