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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff5f1e649-5b7b-4bf6-b571-803a1adb8464%2F5ec9dfb2-8a3a-4fb5-b5ea-4bec1c7cf3db%2Fyglq3i_processed.png&w=3840&q=75)
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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