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Consider the initial value problem y(0) = 1, y'(0) = -1 y" + xy' + 3y = 0, The point x = 0 is an ordinary point of the DE and the equation has power series solutions 8 Σ anx" n=1 (a) The recurrence relation between the coefficients of the power series is given by OA y(x) =a + a₁x+₂x² + OB. O C. O D. OB. an+2=- O C. an+1 = D. an+2 2 an+1 = www. n+3 (n+ 2)(n+1) an n+3 n+1 an (n + 2)(n+1) n+3 n+1 n+3 3 ªn O E. None of the above answers is cotrrect for nz 0 2 (b) The first four terms of the series solution of the IVP are OA 3 2 3 y(x)=1-x-2 X+X+ -an for n≥ 0 for n 20 1 2 y(x)=1+3x+6 3x+x² - 10 y(x) = 1 + 3x + 6x² + 1FX8 2 for nz 0 3 X 2 2 y(x)=1+x+3x²+³x²+ y(x) = 1 +x+ +

Consider the initial value problem y(0) = 1, y'(0) = -1 y" + xy' + 3y = 0, The point x = 0 is an ordinary point of the DE and the equation has power series solutions 8 Σ anx" n=1 (a) The recurrence relation between the coefficients of the power series is given by OA y(x) =a + a₁x+₂x² + OB. O C. O D. OB. an+2=- O C. an+1 = D. an+2 2 an+1 = www. n+3 (n+ 2)(n+1) an n+3 n+1 an (n + 2)(n+1) n+3 n+1 n+3 3 ªn O E. None of the above answers is cotrrect for nz 0 2 (b) The first four terms of the series solution of the IVP are OA 3 2 3 y(x)=1-x-2 X+X+ -an for n≥ 0 for n 20 1 2 y(x)=1+3x+6 3x+x² - 10 y(x) = 1 + 3x + 6x² + 1FX8 2 for nz 0 3 X 2 2 y(x)=1+x+3x²+³x²+ y(x) = 1 +x+ +

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 49E
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Consider the initial value problem y(0) = 1, y'(0) = − 1 y" + xy + 3y = 0, The point x = 0 is an ordinary point of the DE and the equation has power series solutions DO an y(x) = a + a₁x+a₂x²+. Σ ax" n=1 (a) The recurrence relation between the coefficients of the power series is given by OA OB. O C. OD. OB. OC. n+3 an+2=(n+2)(n+1)an for nz 0 n+3 an an+1 = n+1³n OD. an+2 (n+2)(n+1) n+3 n+3ªn for n 20 OE. None of the above answers is cotrrect (b) The first four terms of the series solution of the IVP are OA 3 - for nz 0 23 y(x)=1-x-x+ x² 3 -an for nz 0 1 y(x) = 1 + x + x² 6 2 y(x) = 1 + 3x + 6x² + W|N 3 3 3 1 y(x) = 1 +x+ OE. None of the given answers is correct IKKE
Transcribed Image Text:Consider the initial value problem y(0) = 1, y'(0) = − 1 y" + xy + 3y = 0, The point x = 0 is an ordinary point of the DE and the equation has power series solutions DO an y(x) = a + a₁x+a₂x²+. Σ ax" n=1 (a) The recurrence relation between the coefficients of the power series is given by OA OB. O C. OD. OB. OC. n+3 an+2=(n+2)(n+1)an for nz 0 n+3 an an+1 = n+1³n OD. an+2 (n+2)(n+1) n+3 n+3ªn for n 20 OE. None of the above answers is cotrrect (b) The first four terms of the series solution of the IVP are OA 3 - for nz 0 23 y(x)=1-x-x+ x² 3 -an for nz 0 1 y(x) = 1 + x + x² 6 2 y(x) = 1 + 3x + 6x² + W|N 3 3 3 1 y(x) = 1 +x+ OE. None of the given answers is correct IKKE
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