1) Since P(x) = or Q(x) = are not analytic at x = 0, x = is a singular point of the differential equation. Using F heorem, we must check that xP(x) = and x? Q(x) = are both analytic at x = 0. Since xP(x) and x² Q(x) are analyt = 0 is a regular singular point for the differential equation 7xy" - y + 10y = 0. From the result of Frobenius' Theorem, we may assume xy" – y + 10y = 0 has a solution of the form y = x' E Cnx" which converges for x E (0, R) where r and R are constants that will be c n=0 ater.
1) Since P(x) = or Q(x) = are not analytic at x = 0, x = is a singular point of the differential equation. Using F heorem, we must check that xP(x) = and x? Q(x) = are both analytic at x = 0. Since xP(x) and x² Q(x) are analyt = 0 is a regular singular point for the differential equation 7xy" - y + 10y = 0. From the result of Frobenius' Theorem, we may assume xy" – y + 10y = 0 has a solution of the form y = x' E Cnx" which converges for x E (0, R) where r and R are constants that will be c n=0 ater.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:7xy" – y + 10y = 0.
(1) Since P(x) =
or Q(x) =
are not analytic at x = 0, x =
is a singular point of the differential equation. Using Frobenius'
Theorem, we must check that xP(x) =
and x? Q(x) =
are both analytic at x = 0. Since xP(x) and x² Q(x) are analytic at x = 0,
x = 0 is a regular singular point for the differential equation 7xy" – y + 10y = 0. From the result of Frobenius' Theorem, we may assume that
00
7xy" – y + 10y = 0 has a solution of the form y = x" E C,x" which converges for x E (0, R) where r and R are constants that will be determined
n=0
later.
(2) Substituting y = x" , Cn x" into 7xy" – y + 10y = 0, we get that
00
+
n=0
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 find the indicial roots and the recurrence relation of the differential equation.
(a) From the equation above, we know that the indicial roots of the differential equation are (in increasing order) r =
and r =
(b) From the series above, we find that the recurrence relation is
for
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!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
