Mathematics Exam > Mathematics Questions > If (c1 + c2 In x) /x is the general solution ...
Start Learning for Free
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?
| FREE This question is part of | Download PDF Attempt this Test |
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.
|
Explore Courses for Mathematics exam
|
|
Similar Mathematics Doubts
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?
Question Description
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?.
Solutions 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? in English & in Hindi are available as part of our courses for Mathematics.
Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice Mathematics tests.
|
|
Explore Courses for Mathematics exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup