In this problem you will solve the differential equation(x? + 11)y" + 5xy – y = 0.(1) By analyzing the singular points of the differential equation, we know that a series solution of the form y = Eo Cn x" for the differential equation will converge at least on the interval(2) Substituting y = Eo Cn x" into (x + 11)y" + 5xy' – y = 0. you get that00Σn-2n-1(x2 + 11)n(n-1)+5x1Xn= 2nn= 1n=0Multiplying the coefficients in x through the sums00n-2n(n-1)11n(n-1)n(n-1)1CX.Xn=n=n=nn21Reindex the sumsn(n-1)X.11(n+2)n8n1= 0n=n=n=n=nn+2n2Finally combine the sums Finally combine the sumsx" = 0n=The subscripts on the c's should be increasing and numbers or in terms of n.(3) In this step we will use the equation above to solve for some of the terms in the series and find the recurrence relation.(a) From the constant term in the series above, we know that%3D(b) From the coefficient of r in the series above, we know thatngulan Sp%3D(c) From the series above, we find that the recurrence relation isCfor(4) The general solution to (x? + 11)y" + 5xy'-y = 0 converges at least onand isy = Co76 +..+ Cj+..(5) Solve the initial value problem(x2 + 11)y" + 5xy - y = 0y(0) = -1y(0)= -4y =x2+T' +...

Given , Differential equation is x2+11y"+5xy'-y=0⇒y"+5xx2+11y'-yx2+11=0 1) To find :…

(x? + 11)y" + 5y-y = 0. (1) By analyzing the singular points of the differential equation, we know that a series solution of the form y = E o Cn x" for the differential equation will converge at least on the interval (2) Substituting y = n " into (z? + 11)y" + 5xy' - y = 0. you get that 00 n-2 n-1 (z2 + 11) n= 2 n(n-1) +5x = 0 n n=1 n n=0 Multiplying the coefficients in x through the sums n-2 11n(n-1) n(n-1) n(n-1) X 1 =D0 n= n= n 2 2 1 Reindex the sums 00 00 n n(n-1) 11(n+2)n 8n = 0 X 1 n= n%3= n n+2 n 2 1 Finally combine the sums

(x? + 11)y" + 5y-y = 0. (1) By analyzing the singular points of the differential equation, we know that a series solution of the form y = E o Cn x" for the differential equation will converge at least on the interval (2) Substituting y = n " into (z? + 11)y" + 5xy' - y = 0. you get that 00 n-2 n-1 (z2 + 11) n= 2 n(n-1) +5x = 0 n n=1 n n=0 Multiplying the coefficients in x through the sums n-2 11n(n-1) n(n-1) n(n-1) X 1 =D0 n= n= n 2 2 1 Reindex the sums 00 00 n n(n-1) 11(n+2)n 8n = 0 X 1 n= n%3= n n+2 n 2 1 Finally combine the sums

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: Find two power series solutions of the given differential equation about the ordinary point x = 0.…

Q: 5) Y(x) satisfies the differential equation Y" -2xY' -2Y = 0. If Y(0)=1 and Y'(0) = 0: A) Find the…

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

Q: The given family of functions is the general solution of the differential equation on the indicated…

A: Given, To find a member of the family that is a solution of the given initial problem.

Q: i, I tried to solve this differential equation involving series methods, but I think the a2, a3, a4…

Q: Solve the differential equation 10y"+5xy' -20y = 0 using power series method. Then evaluate the…

Q: Find the indicated coefficients of the power series solution about x = 0 of the differential…

Q: y = c,e* + cze*, (-00, 00); y" – y = 0, y(0) = 0, y'(0) = 1

A: Solution

Q: The point x = 0 is a regular singular point of the given differential equation. 3x²y" - xy + (x² +…

A: Given 3x2y''-xy'+x2+1y=0

Q: Consider the differential equation x²y" – 5xy' – 2xy + 9y = 0. Find one series solution by using the…

Q: Find the two power series solutions of a given differential equation about the ordinary point x=0.…

Q: (5) Solve the initial value problem. x² + 3x + 2 y-2 y' = " y(1) = 4.

Q: 5) Find two power series solutions of the differential equation 2y"-xy=0. The solution should be in…

Q: For the differential equation below, which arises in physics and many other places, (1-x²)y" - 2xy +…

Q: х?у" - ху + (1 - х)у%3D 0,

Q: Match the differential equation with it's particular solution form. | y’’ – 6y' + 9y а. Ate 2t |y'’…

A: We have to match the following differential equation with it's particular solution form.

Q: у" — Зу" + Зу' — у %3D х — 4е* -

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 3) Consider the differential equation 2xy" + y' + y = 0 Find a series solution centered at the…

A: We first assume the series solution of the given differential equation and then find the indicial…

Q: The given family of functions is the general solution of the differential equation on the indicated…

Q: Find the first three nonzero of each linearly independent power series solution around x, =0 for y"…

A: given second order equation y''+x2y'+xy=0 find the first three nonzero of each linearly independent…

Q: Seek a power series solution of the differential equation (x^2 + 2)y′′−4xy′+ 6y= 0

Q: Find the indicated coefficients of the power series solution about x = 0 of the differential…

A: Please find the answer in the next step.zExplanation::

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

In this problem you will solve the differential equation
(x? + 11)y" + 5xy – y = 0.
(1) By analyzing the singular points of the differential equation, we know that a series solution of the form y = Eo Cn x" for the differential equation will converge at least on the interval
(2) Substituting y = Eo Cn x" into (x + 11)y" + 5xy' – y = 0. you get that
00
Σ
n-2
n-1
(x2 + 11)
n(n-1)
+5x
1
X
n= 2
n
n= 1
n=0
Multiplying the coefficients in x through the sums
00
n-2
n(n-1)
11n(n-1)
n(n-1)
1
C
X.
X
n=
n=
n=
n
n
2
1
Reindex the sums
n(n-1)
X.
11(n+2)n
8n
1
= 0
n=
n=
n=
n=
n
n+2
n
2
Finally combine the sums

Finally combine the sums
x" = 0
n=
The subscripts on the c's should be increasing and numbers or in terms of n.
(3) In this step we will use the equation above to solve for some of the terms in the series and find the recurrence relation.
(a) From the constant term in the series above, we know that
%3D
(b) From the coefficient of r in the series above, we know that
ngulan Sp
%3D
(c) From the series above, we find that the recurrence relation is
C
for
(4) The general solution to (x? + 11)y" + 5xy'-y = 0 converges at least on
and is
y = Co
76 +..
+ Cj
+..
(5) Solve the initial value problem
(x2 + 11)y" + 5xy - y = 0
y(0) = -1
y(0)
= -4
y =
x2+
T' +...

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Trending now

This is a popular solution!

Step by step

Solved in 7 steps

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

Determine the Hermite differential equation's power series solution y' - 2xy' + 2ky Please write down the general solution in the form y = C1y1 + C2Y2
Q3. Consider the differential equation x²y" – 5xy' – 2xy + 9y = 0. (а) Find one series solution by using the method of Frobenius. Leave your answer until the first three non-zero terms.
Find the indicated coefficients of the power series solution about 0 of the differential equation a = y=3x+ 3/2 x²+5/2 (x2x+1)y" y' - 5y = 0, y(0) = 0, y'(0) = 3 3 4 x+7/12 +-1/6 5 +0(x)
The point x = O is a regular singular point of the given differential equation. Find the recursive relation for the series solution of the DE below. Show the substitution and all the steps to obtain the recursive relation. Do not solve the equation for y=y(x) xy" + 4y' - xy = 0,
The given family of functions is the general solution of the differential equation on the indicated interval. Find a member of the family that is a solution of the initial-value problem. y=c₁ex + c₂e-x, (-∞, ∞); y" - y = 0, y(0) = 0, y'(0) = 3 y =