_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 = NU {0}. Find all possible values of A, B, C, D, m, and n.
_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 = NU {0}. Find all possible values of A, B, C, D, m, and n.
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
please solve question 3, and if u would like to help me more, solve question 8 also
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc9dc33d-77aa-45ee-8dbf-d57d45a8a86b%2Fafd513be-7b80-4ff8-a4c9-e25fad50128d%2Fmmgnhv_processed.jpeg&w=3840&q=75)
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.
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