One of the following is a general solution of the homogeneous differential equation y' + y = 0: y = Ae + Be , Ax + B, A cos(x) + B sin(x). One of the following is a solution to the nonhomogeneous equation y” + y = y = Y Y y = = x sin(x), y = x sin(x) + cos(x) ln(cos(x)). By superposition, the general solution of the equation y" + y = sec(x) is help (formulas) y = = Find the solution satisfying the initial conditions ▼ y(0) = 9, y'(0) = 4. help (formulas) =sec (x):
One of the following is a general solution of the homogeneous differential equation y' + y = 0: y = Ae + Be , Ax + B, A cos(x) + B sin(x). One of the following is a solution to the nonhomogeneous equation y” + y = y = Y Y y = = x sin(x), y = x sin(x) + cos(x) ln(cos(x)). By superposition, the general solution of the equation y" + y = sec(x) is help (formulas) y = = Find the solution satisfying the initial conditions ▼ y(0) = 9, y'(0) = 4. help (formulas) =sec (x):
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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2. Ordinary
![One of the following is a general solution of the homogeneous differential equation \( y'' + y = 0 \):
\[
y = Ae^x + Be^{-x},
\]
\[
y = Ax + B,
\]
\[
y = A \cos(x) + B \sin(x).
\]
One of the following is a solution to the nonhomogeneous equation \( y'' + y = \sec(x) \):
\[
y = x \sin(x),
\]
\[
y = x \sin(x) + \cos(x) \ln(\cos(x)).
\]
By superposition, the general solution of the equation \( y'' + y = \sec(x) \) is
\[
y = \underline{\hspace{2cm}} \quad \text{help (formulas)}
\]
Find the solution satisfying the initial conditions
\[
y(0) = 9, \quad y'(0) = 4.
\]
\[
y = \underline{\hspace{2cm}} \quad \text{help (formulas)}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d6d6ec3-8d2a-4662-b20e-640089acaa34%2Fefd06a15-75e7-4c3c-b786-664858f169e3%2Fe2cgzcx_processed.png&w=3840&q=75)
Transcribed Image Text:One of the following is a general solution of the homogeneous differential equation \( y'' + y = 0 \):
\[
y = Ae^x + Be^{-x},
\]
\[
y = Ax + B,
\]
\[
y = A \cos(x) + B \sin(x).
\]
One of the following is a solution to the nonhomogeneous equation \( y'' + y = \sec(x) \):
\[
y = x \sin(x),
\]
\[
y = x \sin(x) + \cos(x) \ln(\cos(x)).
\]
By superposition, the general solution of the equation \( y'' + y = \sec(x) \) is
\[
y = \underline{\hspace{2cm}} \quad \text{help (formulas)}
\]
Find the solution satisfying the initial conditions
\[
y(0) = 9, \quad y'(0) = 4.
\]
\[
y = \underline{\hspace{2cm}} \quad \text{help (formulas)}
\]
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