5) Y(x) satisfies the differential equationY" -2xY' -2Y = 0. If Y(0) =1 and Y'(0) = 0:A) Find the first five terms of the power series solution, Y(x). (Carry out yourcalculation so that your highest power of the polynomial is x4.)B) Use your polynomial solution in part A to estimate Y(.1).

Consider the differential equation .The given conditions are .We need to find first five terms of…

Answered: 5) Y(x) satisfies the differential…

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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The solution of the differential equation x2y" - 2xy' + 6y = 0 (x > 0) is the function y(x) = C1 y1(x) + C2 y2(x). Find y1(x) and y2(x). Also, find the constants C1 and C2 if y(1) = - 1, y'(1) = 1.
Solve the ordinary differential equation 4x2y” + (1 - 2x)y = 0 . Then evaluate the first four terms of the solution with a rational indicial root at x = 2.9 .
13) The integer n = a) If n = 3 (mod 9), then what is x ? b) If n = 3 (mod 11), then what is x ? Hint for #13: 12700140x3243243 is missing the digit x. Consider the number 1234. By writing each digit in scientific notation, we have 1234 1 x 10³ +2× 10² +3 × 10¹ + 4 × 10⁰ Then notice that 10 = 1 (mod 9). When we reduce mod 9, we obtain 1234 1 x 10³ +2× 10² +3 x 10¹ + 4 x 10⁰ = = 1x 1³ + 2 x 1² + 3 × 1¹ + 4 × 1⁰ = 1+ 2+ 3+ 4 = 10 = 1 (mod 9). Since 10 = -1 (mod 11), when we reduce mod 11, we obtain 1234 1 x 10³ +2× 10² +3 x 10¹ + 4 x 10⁰ = = 1x (-1)³ +2× (-1)² +3 × (-1)¹ +4× (-1)⁰ = -1 + 2-3 + 4 = 2 (mod 11).
Solve the differential equation using the power series method around the ordinary point x = 0 (1 - x)2y'' - (1 - x)y' - y = 0 ; y(0) = y'(0) = 1
Solve the differential equation 1. y' + 2 sin 2TTX 2. y' = ½ (y2-1) 3. 2хy 3 6x?(x?+2)12
Let the differential equation xy'' + 3y = 0. (a) What are the ordinary points of the differential equation? (b) Use the change of variable t = x − 1 to rewrite the differential equation as a second-order differential equation involving t and y(t). (c) Find a power series solution of the differential equation you obtained in part (b) about t0 = 0. Find the first five terms only. (d) Guess a power series solution to the differential equation xy''+ 3y = 0 of the form y = X∞ n=0 an(x − 1)n (the first five terms only).

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5) Y(x) satisfies the differential equation Y" -2xY' -2Y = 0. If Y(0)=1 and Y'(0) = 0: A) Find the first five terms of the power series solution, Y(x). ( Carry out your calculation so that your highest power of the polynomial is x4.) B) Use your polynomial solution in part A to estimate Y(.1).