1. z1(x) = 3x2 +xe®, z2(x) = xe² – x² are solutions of a second order, linear nonhomogeneous equation L[y] = f(x). Y1(x) = x* is a solution of the corresponding reduced equation L[y] = 0. The general solution of L[y] = f(x) is: (a) z = C1a* + C2x² + xe²
1. z1(x) = 3x2 +xe®, z2(x) = xe² – x² are solutions of a second order, linear nonhomogeneous equation L[y] = f(x). Y1(x) = x* is a solution of the corresponding reduced equation L[y] = 0. The general solution of L[y] = f(x) is: (a) z = C1a* + C2x² + xe²
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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Question 1 and 2.
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![1. z1 (x) = 3x²+xe", z2(x) = xe – x² are solutions of a second order, linear nonhomogeneous
equation L[y]
L[y] = 0. The general solution of L[y] = f(x) is:
f (x). y1 (x) = x* is a solution of the corresponding reduced equation
(a) z =
C1x* + C2x² + xe*
C1a* + C2x2 + C3xe"
(c) z= C1xª + C2(x² + xe")
(b) z =
C1x* + C2xe" + 5x²
= z (p)
(e) None of the above.
2. z1(x) = 2x? + 2 sin 2x, z2(x)
of a second order, linear nonhomogeneous equation L[y] = f(x). The general solution of
L[y] = f(x) is:
x2 + 2 sin 2x, z3(x) = x³ + 2x2 + 2 sin 2x are solutions
=
(а) 2 —
C1 (2x? + 2 sin 2x) + C2 (x³ + 2x² + 2 sin 2x)
(b) z =
C1x? + C2x° + C3 sin 2x
(c) z = C1x² + C2x³ + 2 sin 2x
C1 sin 2x + C2x³ + 2x²
(d) z =
(e) None of the above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe190adae-ee45-49d2-b07b-48740048bea4%2Fd97140eb-0b65-43c1-a871-d87daeb77eb8%2Fe6byvx4_processed.png&w=3840&q=75)
Transcribed Image Text:1. z1 (x) = 3x²+xe", z2(x) = xe – x² are solutions of a second order, linear nonhomogeneous
equation L[y]
L[y] = 0. The general solution of L[y] = f(x) is:
f (x). y1 (x) = x* is a solution of the corresponding reduced equation
(a) z =
C1x* + C2x² + xe*
C1a* + C2x2 + C3xe"
(c) z= C1xª + C2(x² + xe")
(b) z =
C1x* + C2xe" + 5x²
= z (p)
(e) None of the above.
2. z1(x) = 2x? + 2 sin 2x, z2(x)
of a second order, linear nonhomogeneous equation L[y] = f(x). The general solution of
L[y] = f(x) is:
x2 + 2 sin 2x, z3(x) = x³ + 2x2 + 2 sin 2x are solutions
=
(а) 2 —
C1 (2x? + 2 sin 2x) + C2 (x³ + 2x² + 2 sin 2x)
(b) z =
C1x? + C2x° + C3 sin 2x
(c) z = C1x² + C2x³ + 2 sin 2x
C1 sin 2x + C2x³ + 2x²
(d) z =
(e) None of the above.
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