sod geSave AnIn solving a differential equation by Frobenius method of series solution about x = 0, we obtain the following indicialequation and recurrence relation: (2r-1)=0 and C+1" 3n wheren-0,1,2,3,.. Find the solution corresponding to the larger root of the indicial equation. Include the first three nonzeroCOterms, use Co=1OBY=1+x+?1+Ex+

An equation which involves derivative of unknown function is called the differential equation. If…

In solving a differential equation by Frobenius method of series solution about x = 0, we obtain the following indicial equation and recurrence relation: (2r-1)=0 and C1" where n-0,1,2,3,. Find the solution corresponding to the larger root of the indicial equation. Include the first three nonzero terms, use Co=1. /2 OBY-1+*+ 11

In solving a differential equation by Frobenius method of series solution about x = 0, we obtain the following indicial equation and recurrence relation: (2r-1)=0 and C1" where n-0,1,2,3,. Find the solution corresponding to the larger root of the indicial equation. Include the first three nonzero terms, use Co=1. /2 OBY-1+*+ 11

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 Legendre’s differential equation is (1 − x2)y'' − 2xy' + l(l + 1)y = 0, where l is a constant, and y = y(x). Consider a series solution about the point x = 0 of the form provided, where k is a constant and the an are coefficients that need to be determined. Show that the recurrence relation is given by an+2 (n + k + 2)(n + k + 1) = an [(n + k)(n + k + 1) − l(l + 1)].
Find singular points of the differential equation 2x2y′′ − xy′ + (1 + x)y = 0, and solve it around that singular points using power series solutions. Find the first three nonzero terms in each of two solutions about the singular point. Solve the recurrence relation you find (i.e express an in terms of n) and finally show that solutions you find is converging. (Hint: Find the roots of indicial equation and construct the recurrence relation).
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1.) Given xy^''+2y^'-y=0 solve by the method of Frobenius when r=1 and conclude whether r=1 is correct value or can be used to solve the differential equation. After identifying the first three terms, which will become the leader of the REMAINING SERIES? Show how the 2 other series will become a member of the REMAINING SERIES Calculate the RECURRENCE FORMULA: the values of a3, a4, & a5 Conclusion: Is the proper value obtained from the indicial equation? Yes or no, briefly explain.
I know the answer is x+(1/2)(x^2)+(1/2)(x^3)+(13/24)(x^4)+(11/15)(x^5) but can you help me on verifying the answer? Somehow it matches the original equation is what I'm looking for.
Find the general solutions in powers of x and state the recurrence relation: (2 - x2)y" - xy' + 16y = 0
2- Consider the differential equation (²+3)y" - 4y' = 0. The recurrence relation for the coefficients an of the power series solution an" about the ordinary point o=0 is given by b) an+2= an+2= an+2= none of these an+2= 12-0 4nan+1 + (n² = n)an 3n² +9n+6 n22 (4n+4)an+1-(n² - n)an 3n² +9n+6 (n + 4)an+1 +n²an 3n² +9n+6 an+1 + (n²-n)an 3n² +9n+6 1 " n>2 n≥ 2 n22
Find a fundamental set of Frobenius solutions of (4х + х3)у" + (2+ 6х?)у' + 4ху 3— 0 and write the explicit formulas for the coefficients in these series.
Find the recurrence relation of the coefficients for the two linearly independent power series solutions for the differential equation: y" + 2xy' + 4y = 0
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