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Given the Euler's equation x²y" + 3xy' + 4y = 0. 9. Solve for the roots of the indicial equation. O-1+ 3i 01, 3 О-1,3 О -3, — 3 10. Find the general solution of the given Euler's equation. Oy(x) = c1x + caº -1 Oy(x) = c1x -3 = c1x - 3 ]n ¤ + c2x O y(x) O y(x) = -1 1 = c1x¯ cos (V3 ln æ) + c2¤ sin(v3 ln a)

Given the Euler's equation x²y" + 3xy' + 4y = 0. 9. Solve for the roots of the indicial equation. O-1+ 3i 01, 3 О-1,3 О -3, — 3 10. Find the general solution of the given Euler's equation. Oy(x) = c1x + caº -1 Oy(x) = c1x -3 = c1x - 3 ]n ¤ + c2x O y(x) O y(x) = -1 1 = c1x¯ cos (V3 ln æ) + c2¤ sin(v3 ln a)

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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Given the Euler's equation x²y" + 3xy' + 4y = 0. 9. Solve for the roots of the indicial equation. O-1+ V3i O1, 3 О -1, 3 О-3, — 3 6. 10. Find the general solution of the given Euler's equation. O y(æ) = O y(x) = c1x = C1x + c2x°3 1 Oy(x) = c1x + c2x -3 In x 1 = cjx cos (v3 ln x) + c2æ -1 O y(x) = sin (v3 In a)
Transcribed Image Text:Given the Euler's equation x²y" + 3xy' + 4y = 0. 9. Solve for the roots of the indicial equation. O-1+ V3i O1, 3 О -1, 3 О-3, — 3 6. 10. Find the general solution of the given Euler's equation. O y(æ) = O y(x) = c1x = C1x + c2x°3 1 Oy(x) = c1x + c2x -3 In x 1 = cjx cos (v3 ln x) + c2æ -1 O y(x) = sin (v3 In a)
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