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Consider the following differential equation (4-x)y"+y = 0, 0 = 0. (a) Seek a power series solution for the given differential equation about the given point vo; find the recurrence relation that the coefficients must satisfy. TU -1 ✓ On+2= an+1+ are n = 0, 1, 2,... 4 (n + 2) 4 (n+2)(n+1) (b) Find the first four nonzero terms in each of two solutions y₁ and 32. NOTE: For y, set ap = 1 and a, = 0 in the power series to find the first four - 1 in the power series to find non-zero terms. For yz. set ay = 0 and a the first four non-zero terms. 1 1 1 5 X 1(x) = 1 7,² 73 + 2²+ 25 8 96 4768 15360 1 1 1 X Y₂(x)=x 24 192 3840 (c) By evaluating the Wronskian W (y₁, 32) (zo), show that y₁ and yż form a fundamental set of solutions. 1 0 ✓ W (y1, y2) (0) = 0 1 x³ 24 2:5

Consider the following differential equation (4-x)y"+y = 0, 0 = 0. (a) Seek a power series solution for the given differential equation about the given point vo; find the recurrence relation that the coefficients must satisfy. TU -1 ✓ On+2= an+1+ are n = 0, 1, 2,... 4 (n + 2) 4 (n+2)(n+1) (b) Find the first four nonzero terms in each of two solutions y₁ and 32. NOTE: For y, set ap = 1 and a, = 0 in the power series to find the first four - 1 in the power series to find non-zero terms. For yz. set ay = 0 and a the first four non-zero terms. 1 1 1 5 X 1(x) = 1 7,² 73 + 2²+ 25 8 96 4768 15360 1 1 1 X Y₂(x)=x 24 192 3840 (c) By evaluating the Wronskian W (y₁, 32) (zo), show that y₁ and yż form a fundamental set of solutions. 1 0 ✓ W (y1, y2) (0) = 0 1 x³ 24 2:5

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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Consider the following differential equation (4-x)y"+y = 0, 0 = 0. (a) Seek a power series solution for the given differential equation about the given point vo; find the recurrence relation that the coefficients must satisfy. TU -1 ✓ On+2= a₁ +1 + a n= 0, 1, 2,... 4 (n + 2) 4(n+2)(n+1) (b) Find the first four nonzero terms in each of two solutions y₁ and 32. NOTE: For y, set ap = 1 and a, = 0 in the power series to find the first four non-zero terms. For yz. set ay = 0 and a = 1 in the power series to find the first four non-zero terms. 1 1 1 5 X 1(x) = 1 2.² 7.3 + 2²+ 25 8 96 4768 15360 1 1 1 X Y₂(x)=x 24 192 3840 (c) By evaluating the Wronskian W (y₁, 32) (zo), show that y₁ and yź form a fundamental set of solutions. 1 0 ✓ W (y1, y2) (0) = 0 1 x³ 2.5
Transcribed Image Text:Consider the following differential equation (4-x)y"+y = 0, 0 = 0. (a) Seek a power series solution for the given differential equation about the given point vo; find the recurrence relation that the coefficients must satisfy. TU -1 ✓ On+2= a₁ +1 + a n= 0, 1, 2,... 4 (n + 2) 4(n+2)(n+1) (b) Find the first four nonzero terms in each of two solutions y₁ and 32. NOTE: For y, set ap = 1 and a, = 0 in the power series to find the first four non-zero terms. For yz. set ay = 0 and a = 1 in the power series to find the first four non-zero terms. 1 1 1 5 X 1(x) = 1 2.² 7.3 + 2²+ 25 8 96 4768 15360 1 1 1 X Y₂(x)=x 24 192 3840 (c) By evaluating the Wronskian W (y₁, 32) (zo), show that y₁ and yź form a fundamental set of solutions. 1 0 ✓ W (y1, y2) (0) = 0 1 x³ 2.5
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