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If (c1 + c2 In x) /x is the general solution of the differential equation 
x > 0, then k equals
Correct answer is '-1'. Can you explain this answer?
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Verified Answer
If (c1 + c2 In x) /x is the general solution of the differential equat...
The operator form of differential equation is (x2D2 + KxD + 1)y = 0 ...(1)
Let x = et ⇒ t = log x
x2D2 ≡ D′(D′ – 1) D′ ≡ d / dt xD ≡ D′
then subsituting x2D2 and xD in equation (1), we get
[D′(D – 1) + KD′ + 1]y = 0
[D′2 + (K – 1) D′ + 1]y = 0
A.E. is m2 + (K – 1)m + 1 = 0
Solution of (1) is
y = (c1 + c2 log x) / x = (c1 + c2 t) e – t
⇒ K = – 1.
Let x = et ⇒ t = log x
x2D2 ≡ D′(D′ – 1) D′ ≡ d / dt xD ≡ D′
then subsituting x2D2 and xD in equation (1), we get
[D′(D – 1) + KD′ + 1]y = 0
[D′2 + (K – 1) D′ + 1]y = 0
A.E. is m2 + (K – 1)m + 1 = 0
Solution of (1) is
y = (c1 + c2 log x) / x = (c1 + c2 t) e – t
⇒ K = – 1.
Most Upvoted Answer
If (c1 + c2 In x) /x is the general solution of the differential equat...
The operator form of differential equation is (x2D2 + KxD + 1)y = 0 ...(1)
Let x = et ⇒ t = log x
x2D2 ≡ D′(D′ – 1) D′ ≡ d / dt xD ≡ D′
then subsituting x2D2 and xD in equation (1), we get
[D′(D – 1) + KD′ + 1]y = 0
[D′2 + (K – 1) D′ + 1]y = 0
A.E. is m2 + (K – 1)m + 1 = 0
Solution of (1) is
y = (c1 + c2 log x) / x = (c1 + c2 t) e – t
⇒ K = – 1.
Let x = et ⇒ t = log x
x2D2 ≡ D′(D′ – 1) D′ ≡ d / dt xD ≡ D′
then subsituting x2D2 and xD in equation (1), we get
[D′(D – 1) + KD′ + 1]y = 0
[D′2 + (K – 1) D′ + 1]y = 0
A.E. is m2 + (K – 1)m + 1 = 0
Solution of (1) is
y = (c1 + c2 log x) / x = (c1 + c2 t) e – t
⇒ K = – 1.
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If (c1 + c2 In x) /x is the general solution of the differential equation x > 0, then k equalsCorrect answer is '-1'. Can you explain this answer?
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If (c1 + c2 In x) /x is the general solution of the differential equation x > 0, then k equalsCorrect answer is '-1'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about If (c1 + c2 In x) /x is the general solution of the differential equation x > 0, then k equalsCorrect answer is '-1'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If (c1 + c2 In x) /x is the general solution of the differential equation x > 0, then k equalsCorrect answer is '-1'. Can you explain this answer?.
If (c1 + c2 In x) /x is the general solution of the differential equation x > 0, then k equalsCorrect answer is '-1'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about If (c1 + c2 In x) /x is the general solution of the differential equation x > 0, then k equalsCorrect answer is '-1'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If (c1 + c2 In x) /x is the general solution of the differential equation x > 0, then k equalsCorrect answer is '-1'. Can you explain this answer?.
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