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2y=0 and assume a solution of th wen by: A) cn=0.1.2.... +n point. point. pint. iven by: nt. -). 1+n n=0,1,2,...

2y=0 and assume a solution of th wen by: A) cn=0.1.2.... +n point. point. pint. iven by: nt. -). 1+n n=0,1,2,...

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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## Differential Equation Problem **Given the differential equation:** \[ (1+x^2)y'' + 2xy' - 2y = 0 \] **Assume a solution of the form:** \[ y = \sum_{n=0}^{\infty} c_n x^n \] **Choose All Correct Answers Below:** **Option A:** The recurrence relation is given by: \[ c_{n+2} = \left(\frac{1-n}{1+n}\right) c_n , \quad n=0,1,2,\ldots \] **Option B:** \( x = -1 \) is an ordinary point. **Option C:** \( x = -1 \) is a singular point. **Option D:** \( y = c_0 \left( 1 + x \arctan(x) \right) + c_1 x \) **Option E:** \( x = 1 \) is an ordinary point. **Option F:** The recurrence relation is given by: \[ c_{n+2} = \left(\frac{n}{1+n}\right) c_n , \quad n=0,1,2,\ldots \] **Option G:** \( y = c_0 \arctan(x) + c_1 x^2 \) **Option H:** \( x = 1 \) is a singular point.
Transcribed Image Text:## Differential Equation Problem **Given the differential equation:** \[ (1+x^2)y'' + 2xy' - 2y = 0 \] **Assume a solution of the form:** \[ y = \sum_{n=0}^{\infty} c_n x^n \] **Choose All Correct Answers Below:** **Option A:** The recurrence relation is given by: \[ c_{n+2} = \left(\frac{1-n}{1+n}\right) c_n , \quad n=0,1,2,\ldots \] **Option B:** \( x = -1 \) is an ordinary point. **Option C:** \( x = -1 \) is a singular point. **Option D:** \( y = c_0 \left( 1 + x \arctan(x) \right) + c_1 x \) **Option E:** \( x = 1 \) is an ordinary point. **Option F:** The recurrence relation is given by: \[ c_{n+2} = \left(\frac{n}{1+n}\right) c_n , \quad n=0,1,2,\ldots \] **Option G:** \( y = c_0 \arctan(x) + c_1 x^2 \) **Option H:** \( x = 1 \) is a singular point.
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