1. Calculate by the Power Series Method the value of y as general solution(term-by-term from n = 0 to n = 4) of the following ordinarydifferential equation:(10 – x2)y" + 5xy+ y = 0

Second order differential equations,with Power series method

Answered: 1. Calculate by the Power Series Method…

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 differential equation which has a regular singular point at a = with roots (in increasing order) r1 - 2x(x1)y" +3(x − 1)y - y = 0 0. The indicial equation for x = 0 is and r2 x²+ r+ = 0 Find the indicated terms of the following series solutions of the differential equation: (a) y (6+ x+ x²+ 23+ 2+...) x²+ x3+ 2₁+...) (b) y=(7+ x+ The closed form of solution (a) is y =
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Diff eqns
Question 1: The general power series solution about the ordinary point x=0 of the differential equation y"-xy'-y = 0 is: y(x) = co (1 +++ ) + G₁₂(x + — + ...) b. y = co (1+²+) + c₂ (x + 2+ ) y = co ( + ) + ₂(x + 12 + -) c. d. None of them
1- Explain the the difference between DE with Ordinary points and DE with singular points Find two power series solutions of the given differential equation about the ordinary point x = 0o. y" - 4xy' + y = 0 We are asked to find two power series solutions to the following homogenous linear second-order differential equation. y" - 4xy' + y = 0 By Theorem 6.2.1, we know two such solutions exist about the ordinary point x = 0. In fact, the differential equation has no singular points as each of the coefficient functions are (very simple) polynomials. Therefore, they are trivially represented as power series at any point and are therefore analytic. This means the power series solution will converge for |x| < oo. Let y = 5C". We substitute this series and its derivatives into the given differential equation. We will n = 0 solve for two sets of cn to find the two solutions. The differential equation includes non-zero terms for the first and second derivative of y. These derivatives always…
QUESTION 2 Use the method of the power series to find the first five non-zero terms of the solution of the following second order differential equation: y" + xy=3, y(0) = 0, y'(0) = 1
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1.) Solve the following differential equation for x(1)=1 and h=0.1 using the 4th-degree Runge-Kutta method by advancing 4 iterations. x'=5x + y + 1 2) Advance the same differential equation by two more Iterations with the Adams method. x'=5x + y + 1 *Note: In calculations, 4 digits should be taken after the comma.

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1. Calculate by the Power Series Method the value of y as general solution (term-by-term from n = 0 to n = 4) of the following ordinary differential equation: (10 – x2)y" + 5xy + y = 0