Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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- c) Consider the differential equation 1 y" + y +y = 0. Assuming that the solution can be written as a power series, y = ao + a1x + a2x² + · · · + anx" + . ..= anx" n=0 show that a1 = 0 and that the other constants in this series must satisfy 1 an-2. an Hence derive the power series for y(x) up to and including powers of x6 assuming the constant ao = 1.arrow_forwardFind two power series solutions of the given differential equation about the ordinary point x = 0. y" + x²y = 0 1 4 Oy=1- -X + 12 1 Oy=1-x + 6 14 Oy = 1- x² + 6 O y = 1 + 1 672 14 -x + 1 252 Oy=1++++++ 12 672 1 252 8 1 252 8 8 - and y = x - ... and y =x - + + ... and y = x + and y = x - and y = x + 1 20 1 12 1x5 20 1 -X 12 1 5 -x³ + 12 + +5 + + -X + 1 1440 1 5 ·X 672 1 1440 1 672 1 672 9arrow_forward2,5) Please type answer or make it very easy to readarrow_forward
- xy"+y'=0; y1=ln(x)arrow_forwardFind two power series solutions of the given differential equation about the ordinary point x = 0. (x2+1)y" 6y = 0 Oy₁ = 1 + 3x² + x²-to 1,6 Oy₁ = 1 + 3x² + 5x4 + 7x6 + Oy₁ = 1 + 3x² + x4 + +6 5 + + and y₂ = x + x³ and Y2 = x + 2x³ + 3x5 + 4x7. and y₂ = x - x³ 34 ₁=1+²+x+6+ ... and y₂ = x+3x² Oy₁ = 1 - 3x² + 5x4 – 7x6 + and y₂ = x - 2x³ + 3x5 - 4x² + .arrow_forward
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