Given that y, = In(x) is a particular solution of the non-homogeneous equation x?y" + xy' + y = In(x) and that y, = independent solutions of the associated homogeneous equation x²y" + xy' + y = 0. Which of the following is the general solution of the non-homogeneous equation? a) y = c1 cos(In(x)) + c2 sin(ln(x)) + In(x) b) y = c, cos(In(x)) + c2 sin(In(x)) + czln(x) c) y = c, cos(ln(x)) + c2 sin(ln(x)) d) y = c3 In(x) %3D cos(In(x)) and y2 = sin(In(x)) are linearly %3D
Given that y, = In(x) is a particular solution of the non-homogeneous equation x?y" + xy' + y = In(x) and that y, = independent solutions of the associated homogeneous equation x²y" + xy' + y = 0. Which of the following is the general solution of the non-homogeneous equation? a) y = c1 cos(In(x)) + c2 sin(ln(x)) + In(x) b) y = c, cos(In(x)) + c2 sin(In(x)) + czln(x) c) y = c, cos(ln(x)) + c2 sin(ln(x)) d) y = c3 In(x) %3D cos(In(x)) and y2 = sin(In(x)) are linearly %3D
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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Transcribed Image Text:3. Given that y, = In(x) is a particular solution of the non-homogeneous equation
x²y" + xy' + y = In(x) and that y, = cos(ln(x)) and y, = sin(ln(x)) are linearly
independent solutions of the associated homogeneous equation x²y" + xy' +
y = 0. Which of the following is the general solution of the non-homogeneous
equation?
a) y = c1 cos(In(x)) + c2 sin(In(x)) + In(x)
b) y = c, cos(In(x)) + c2 sin(In(x)) + czln(x)
c) y = c, cos(In(x)) + c2 sin(ln(x))
d) y = c3 In(x)
4. What is the general solution of the following IVP.
y(3) – 5y"-22y'+56y=0
a) y = ce-4t + cze2t + cze7t
b) y = c1e4t + Cze2t + Cze7t
c) yt = C1e-4t + c2e¬2t + C3e7t
d) yt = ce4t + c2e-2t + c3e7t
У (0)%31
y'(0)=-2
y"(0) = -4
5. Evaluate the following differential equation using the Principle of Superposition.
What is its particular solution?
у" — 9у — 0
y(0) = 2
y'(0) = -1
a) y(t) =e
b) y(t) = et +e3
c) y(t) = ?e-3t +e
7.
e3t
-3t
Ee-3t
6
e3t
6
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