If we want to find the solution of the differential equation y- 2.xy = 0 with the help of power series around x, = 0 then Which of the following is the Recurrence Relation to be obtained? 2a, n20 (n+2) 2а, n20 (n+2) 2a n20 (n+1) 2a, a +2 n20 (n+1) 2a,-1 an+1 n20 %3D (n+2)

If we want to find the solution of the differential equation y- 2.xy = 0 with the help of power series around x, = 0 then Which of the following is the Recurrence Relation to be obtained? 2a, n20 (n+2) 2а, n20 (n+2) 2a n20 (n+1) 2a, a +2 n20 (n+1) 2a,-1 an+1 n20 %3D (n+2)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Using the power series method about x = 0, the recurrence relation of the differential equation: y"…

Q: The recurrence relation for the differential equation xy + 2y -xy=0 is Oack(k+r)(k+r-1)-Ck-2=0…

A: Let y= ∑k=0∞akxk+r be the solution of the given differential equation.Here y1= ∑k=0∞ak(k+r)xk+r-1…

Q: 11. Find the Maclaurin series for | cos (2x³) dx. OS

A: here we have to find the intregration

Q: (c) y"(x) + (x - 1) y'(x) + (2x – 1) y(x) = 0 %3D (d) (x² – 1) y" (x) + x y' (x) + 2 y(x) = 0 %3D…

Q: Let y= E a, (x – 1)" be the power series solution to n=0 у - 7у +11x3%0, у(1)— 4. Find ag. 269 a3 3…

A: let y=∑n=0anx-1n be the power series solution to y'-7y+11x3=0 with initial condition y1=4 find the…

Q: Find general solutions in powers of x of the differential equations in Problems through. State the…

Q: Solve the given ODE using the power series method. (22 + 1)y'" + xy' – 4y = 0 4. Obtain the…

Q: Consider the initial value problem y(0) = 1, y'(0) = -1 y" + xy' + 3y = 0, The point x = 0 is an…

Q: Consider the following differential equation: (x² – 4)y" – xy' – 3y = 0 i. Verify that x, = 0 is an…

Q: Find the first four nonzero terms in a power series expansion about x = 0 for a general solution to…

Q: In solving a differential equation by Frobenius method of series solution about x = 0, we obtain the…

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

Q: Find a power series expansion about x = 0 for a general solution to the given differential equation.…

Q: a. Use Power Series to find the solution of the homogeneous DE given by + 3xy = 0. d²y dx² b. Start…

A: Power series solution.

Q: 3. Consider the 2nd order linear ODE: (1-x²)y" - xy' + a²y = 0 (1) where a is a real constant. (a)…

A: The second order linear ODE is where is a real constant.(a) To solve the equation about the…

Q: 5. Find at least first four non-zero terms in a power series expansion about x = 0 for a general…

A: Since you post more than one seperated questions, as per our guideline we can solve only first…

Q: Using the power series method about x = 0, the recurrence relation of the differential equation…

Q: **** If the power series method was used to solve the following D.E (x- 2)(x + 2)y"-y' +y 0 Xo

Q: (z-1)y"+3y-0; y(0)-2,y (0) =3 hot ith A y(x)- 2 1+ 1+3+ - B. y(x) - 2[1++ -3 (a ++ 4 D. u(a)- 21++…

A: Given differential equation is: (x-1)y''+3y=0, y(0)=2,y'(0)=3 Here P0(x)=x-1⇒P0(0)=0-1=-1≠0 Let the…

Q: Find the recurrence relation between the coefficents for the power series solutions to the following…

A: 1. Given DE is y"+xy'+2y=0......(1) Also given x0=0. We find the recurrence relation between the…

Q: Using the power series method about x = 0, the recurrence relation of the differential equation: -…

A: Given differential equation is x2+1y''−4xy+6y=0.......1. We have to find the recurrence relation of…

Q: 2y" – 5 y' = 0, which of the following is the recurrence relation obtained for 2? San-1 A) an…

A: Here first we assume you then find the conditions.

Q: 4n2 +n (a) Check the convergence of the series E using limit comparison test. n=o n°+6n2 – n (b)…

Q: with co - 2. 2y" + (x + 1)y' + 3y = 0, (a) Seek power series solutions of the given differential…

A: (a)The given equation is and Suppose that be the power series solution of (1)…

Q: 3. Consider the differential equation 0 = (1-x²) y" - xy +9y with solution of the form y = Σ anagn…

Q: ∞ If C'(x) => n=0 C(x) – S(x). ∞ n=0 2n 4n² + 1 x 2n ∞ and S(x) => 2n + 1 n=0 (2n + 1)² +1 2n+1 x…

Q: The second order initial value problem below has a power series solution in x. Calculate the first…

A: (.) Given initial value problem is,(.) Power series solution of a differential equation about an…

Q: 8. (10 points) Suppose you were looking for a power series solution of a differential equa- tion…

Q: Suppose that the following initial value problem has a power series solution of the form y = 2n=0 an…

A: We are entitled to solve one question at a time and up to 3 sub parts only . Given - y'' +…

Q: (b) Using Taylor series method to solution of dy =x²-3y, using two loops; where yo 1, x1= 0.1; and…

A: Given, dydx=x2-3yand y(0)=1, x1=0.1 , n=3.

Q: Solve the given ODE using the power series method. y' – xy = 0 2. Obtain the recurrence relation.…

Q: Using the power series method about x = 0, the recurrence relation of the differential %3D equation:…

Q: EXAMPLE 1 Solve the equation y" + y = 0 by the power-series method.

A: In the given question there is a differential equation given and we have to find the solution by…

Q: Find a recurrence formula of the n" coefficient of the power series solution to the differential…

A: First we have to assume general series solution for this given differential equation.

Q: Question 10 (10.1) In solving a differential equation by using the power series method the following…

Q: 4. Use power series to find two linearly independent solutions of this differential equation (x -…

Q: For a power series solution about x=0 for a IVP. The initial conditions are y(0)=8 and y'(0)= -15.…

Q: The Hermite equation is a second order linear homogeneous ordinary differential equation, y" - 2xy +…

A: The given differential equation is y''-2xy'+λy=0 where λ is a real number. Suppose the differential…

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

If we want to find the solution of the differential equation y- 2.xy = 0 with the help of power series around x, = 0
then
Which of the following is the Recurrence Relation to be obtained?
2a,
n20
(n+2)
2а,
n20
(n+2)
2a
n20
(n+1)
2a,
a +2
n20
(n+1)
2a,-1
an+1
n20
%3D
(n+2)

Expert Solution

Step 1-

Step by step

Solved in 4 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

)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 a, 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).
2. Seek a power series solution of the form y(r) =ana" to the differential equation n=0 y"(r) – 2ry (x) – 4y(x) = 0, xo = 0. (a) Set-up a recurrence for the cofficients, an. (b) Find the first four terms of two independent power series solutions yı and y2 in such a way that you can write y(r) = a0y1(x) + a1y2(x). (c) Determine the Taylor series of e about the point ro = 0. %3D (Hint: Use the Taylor series for e".) (d) By using Part(c), find the explicit form of y2(x).
Find a power series expansion about x = 0 for a general solution to the given differential equation. Your answer should include a general formula for the coefficients. -z" -x²z' - xz = 0 What is the power series solution to the differential equation? A. Z(x) = a 1 + B. Z(X) = a1 + ∞ Σ (-1) - n=1 (1.4.7... (3n - 2))² (3n)! ∞ Σ (-1). n=1 ∞ OC. Z(x) = a 1+ Σ n=1 D. Z(X) =a 1+ Σ n=1 (3.6.9...(3n)) (3n - 2)! (1.4.7... (3n - 2))² (3n)! -x³n (3.6.9...(3n)) (3n - 2)! 3n 3n + a X + 2,³^) - ₁,[(x + 2, + x+ Σ n=1 X + x+ Σ n=1 ∞ n=1 (-1)^. ∞ Σ (-1). n=1 (2.5.8...(3n-1))² (3n + 1)! (1.4.7...(3n-2)) +1 (3n + 2)! -x³n+ (2.5.8--- (3n-1))² (3n+ 1)! (1.4.7...(3n-2)) (3n+2)! -x³n+1 -x³n+1 -x³n+ 1
I need detailed explanation solving this problem (c) from Engineering Mathematics, please.
B1. Advance maths
Can you help me with the third part?
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).
2) Suppose you have a differential equation that satisfies the conditions of Theorem 6.2.1- Existence of Power Series Solutions with center x, = 0. It is then guaranteed that a solution exists of the form y(x) = E-0 Cnx". The recurrence relation for the coefficients was calculated to be k 3 Ck+2 k = 1,2,3, .. 2(k + 2) k+1 2(k + 2)(k + 1) 3 C2 = -7C0 Find the solution y(x) to the initial-value problem if y(0) = 0 and y'(0) = 1. Give at least the first 3 nonzero terms of the solution.
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
Hello, I have been struggling to find the k value and recurrence relation for this differential equation using the Frobenius method. Could I please get some help to better understand the learning process?