Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
_Q7) Let y(x) = E=0 Cnx" denote the power series solution of y'(x)- y(x) = x³ with y(0) = 4. Find its general solution. _Q8) Solve using the series solution: xy'(x) sin(x) y(x) = 0.

_Q7) Let y(x) = E=0 Cnx" denote the power series solution of y'(x)- y(x) = x³ with y(0) = 4. Find its general solution. _Q8) Solve using the series solution: xy'(x) sin(x) y(x) = 0.

Advanced Engineering Mathematics
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
icon
Related questions
Question

please sir please solve question 7 and 8

Solve completely the following problems: _Q1) Consider the differential equation y" - = 0. Let y₁ = t + 1 be a solution to the given t+1 ZY (t+1)2- equation. Find a general solution of y" -' + (+1)2 y = 1. + _Q2) Use the method of undetermined coefficients (find the value of the constants) to determine the form of a particular solution for Ay"""+By"" + Cy" = x+e-2x sin(7x), where A,B,C ER and the corresponding homogeneous equation have the roots: r² = 0 and r = -2 ± 7i _Q4) What is the form of the following: a) C{t3 sinh(t)}+£-1 ¹ {35²-65+6) b) L-¹ {In (+3)}. c) sin(t) 8 (5) (t-1)dt. _Q3) If y = x-¹ cos(2 ln(x)) is a solution of Ax³y"" + Bxly(m) + Cxy(n) + Dxy = 0, where A, B, C, D, m, n E NU {0}. Find all possible values of A, B, C, D, m, and n. _Q5) Solve (y")³ = y(1 + (y')²). _Q6) Suppose that a differentiable function y satisfies y(0) = 6 and y'(0) = -1. Furthermore, if L{y}(3) = 1, then what is the value of L{y"}(3)? 00 _Q7) Let y(x) = Σno Cnx" denote the power series solution of y'(x) y(x) = x³ with y(0) = 4. Find its general solution. _Q8) Solve using the series solution: xy'(x) - sin(x) y(x) = 0.
Transcribed Image Text:Solve completely the following problems: _Q1) Consider the differential equation y" - = 0. Let y₁ = t + 1 be a solution to the given t+1 ZY (t+1)2- equation. Find a general solution of y" -' + (+1)2 y = 1. + _Q2) Use the method of undetermined coefficients (find the value of the constants) to determine the form of a particular solution for Ay"""+By"" + Cy" = x+e-2x sin(7x), where A,B,C ER and the corresponding homogeneous equation have the roots: r² = 0 and r = -2 ± 7i _Q4) What is the form of the following: a) C{t3 sinh(t)}+£-1 ¹ {35²-65+6) b) L-¹ {In (+3)}. c) sin(t) 8 (5) (t-1)dt. _Q3) If y = x-¹ cos(2 ln(x)) is a solution of Ax³y"" + Bxly(m) + Cxy(n) + Dxy = 0, where A, B, C, D, m, n E NU {0}. Find all possible values of A, B, C, D, m, and n. _Q5) Solve (y")³ = y(1 + (y')²). _Q6) Suppose that a differentiable function y satisfies y(0) = 6 and y'(0) = -1. Furthermore, if L{y}(3) = 1, then what is the value of L{y"}(3)? 00 _Q7) Let y(x) = Σno Cnx" denote the power series solution of y'(x) y(x) = x³ with y(0) = 4. Find its general solution. _Q8) Solve using the series solution: xy'(x) - sin(x) y(x) = 0.
Expert Solution
steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS