) The indicial equation of (x²-x)y" + 3y' + (x - 1)y = 0 at x = 0 is : (A) r²- 4r=0 (B) ²-4 = 0 (C) r²- 2r=0 (D) ² + 4 = 0 (E) ²-1=0
) The indicial equation of (x²-x)y" + 3y' + (x - 1)y = 0 at x = 0 is : (A) r²- 4r=0 (B) ²-4 = 0 (C) r²- 2r=0 (D) ² + 4 = 0 (E) ²-1=0
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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solve question 8 please
![On this educational webpage, you will find a series of questions and multiple-choice answers related to differential equations and their solutions. Each question asks you to solve for a particular function or equation based on the given conditions.
**Q6) General Solution of Given Differential Equation:**
The general solution of the differential equation
\[ x^2 y'' + 3xy' + y = 0 \]
is \( y(x) = \)
Options:
A) \( c_1 x + c_2 x \ln x \)
B) \( c_1 x + \frac{c_2}{x} \)
C) \( \frac{c_1}{x} + c_2 \ln x \)
D) \( c_1 + c_2 x \)
E) \( c_1 x + c_2 x^2 \)
**Q7) Function of Wronskian and Initial Condition:**
Given the Wronskian \( \mathbf{W}(e^x, f(x)) = e^{3x} \) and initial condition \( f(0) = 4 \), find \( f(x) \):
Options:
A) \( 3e^{2x} + e^x \)
B) \( 2e^x \)
C) \( 4e^{2x} \)
D) \( 3e^x + e^{2x} \)
E) \( 4e^{-2x} \)
**Q8) Indicial Equation:**
The indicial equation of
\[ (x^2 - x)y'' + 3y' + (x - 1)y = 0 \]
at \( x = 0 \) is:
Options:
A) \( r^2 - 4r = 0 \)
B) \( r^2 - 4 = 0 \)
C) \( r^2 - 2r = 0 \)
D) \( r^2 + 4 = 0 \)
E) \( r^2 - 1 = 0 \)
Detailed explanation of each option, the method of solution, and the detailed steps would be provided. For any equation-related diagrams or graphs, they would be illustrated for better understanding.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F232632b1-f2d3-4d97-a5a4-d15def76356a%2Fab8e0298-4188-4348-afab-e45ffe9365ac%2F91jjkpn_processed.png&w=3840&q=75)
Transcribed Image Text:On this educational webpage, you will find a series of questions and multiple-choice answers related to differential equations and their solutions. Each question asks you to solve for a particular function or equation based on the given conditions.
**Q6) General Solution of Given Differential Equation:**
The general solution of the differential equation
\[ x^2 y'' + 3xy' + y = 0 \]
is \( y(x) = \)
Options:
A) \( c_1 x + c_2 x \ln x \)
B) \( c_1 x + \frac{c_2}{x} \)
C) \( \frac{c_1}{x} + c_2 \ln x \)
D) \( c_1 + c_2 x \)
E) \( c_1 x + c_2 x^2 \)
**Q7) Function of Wronskian and Initial Condition:**
Given the Wronskian \( \mathbf{W}(e^x, f(x)) = e^{3x} \) and initial condition \( f(0) = 4 \), find \( f(x) \):
Options:
A) \( 3e^{2x} + e^x \)
B) \( 2e^x \)
C) \( 4e^{2x} \)
D) \( 3e^x + e^{2x} \)
E) \( 4e^{-2x} \)
**Q8) Indicial Equation:**
The indicial equation of
\[ (x^2 - x)y'' + 3y' + (x - 1)y = 0 \]
at \( x = 0 \) is:
Options:
A) \( r^2 - 4r = 0 \)
B) \( r^2 - 4 = 0 \)
C) \( r^2 - 2r = 0 \)
D) \( r^2 + 4 = 0 \)
E) \( r^2 - 1 = 0 \)
Detailed explanation of each option, the method of solution, and the detailed steps would be provided. For any equation-related diagrams or graphs, they would be illustrated for better understanding.
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