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_Q4) What is the form of the following: a) £{t3sinh(t)}+£−1{ to (35²-65+6)

_Q4) What is the form of the following: a) £{t3sinh(t)}+£−1{ to (35²-65+6)

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
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please solve question 4

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.
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