The indicated functions are known linearly independent solutions of the associated homogeneous differential equation on (0, c0). Find the general solution of the given nonhomogeneous equation. x²y" + xy' + y = sec(In(x)); Y1 = cos(In(x)), Y2 = sin(In(x)) y(x) = c,cos(In(x)) + c,sin(In(x))+ln(cos (x)) cos(ln(x)) + In(x)sin(In(x))
The indicated functions are known linearly independent solutions of the associated homogeneous differential equation on (0, c0). Find the general solution of the given nonhomogeneous equation. x²y" + xy' + y = sec(In(x)); Y1 = cos(In(x)), Y2 = sin(In(x)) y(x) = c,cos(In(x)) + c,sin(In(x))+ln(cos (x)) cos(ln(x)) + In(x)sin(In(x))
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![The indicated functions are known linearly independent solutions of the associated homogeneous differential equation on \( (0, \infty) \). Find the general solution of the given nonhomogeneous equation.
\[
x^2 y'' + x y' + y = \sec(\ln(x));
\]
\[
y_1 = \cos(\ln(x)), \quad y_2 = \sin(\ln(x))
\]
\[
y(x) = c_1 \cos(\ln(x)) + c_2 \sin(\ln(x)) + \ln(\cos(x)) \cos(\ln(x)) + \ln(x) \sin(\ln(x))
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2c8a2351-0faf-49df-b50e-203220f7d5bc%2F604ffa0b-49aa-4d13-acd7-afc40eb4a026%2Fmtzs7kr_processed.png&w=3840&q=75)
Transcribed Image Text:The indicated functions are known linearly independent solutions of the associated homogeneous differential equation on \( (0, \infty) \). Find the general solution of the given nonhomogeneous equation.
\[
x^2 y'' + x y' + y = \sec(\ln(x));
\]
\[
y_1 = \cos(\ln(x)), \quad y_2 = \sin(\ln(x))
\]
\[
y(x) = c_1 \cos(\ln(x)) + c_2 \sin(\ln(x)) + \ln(\cos(x)) \cos(\ln(x)) + \ln(x) \sin(\ln(x))
\]
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