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Consider the 2nd order Cauchy-Euler differential equation
Then the values of λ for which all the solutions of above DE tends to 0 as x →∞ , is
- a)λ > 0
- b)λ ≥ 1
- c)λ ≥ 0
- d)No such λ exist
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Consider the 2nd order Cauchy-Euler differential equationThen the valu...
Let z = log x => x = e2
Put these values in given DE. we have,
Case -1 when 25 - 24λ > Qthen soln is given by,
Where c1 and c2 are arbitrary finite constants. Now we want when x → ∞ then y(x) -> 0 .
Now take
Now take
So in this case limit not exist.
So now no need to consider further case.
Now we can say no % exist for which all the soln tends to 0 as x → ∞
Most Upvoted Answer
Consider the 2nd order Cauchy-Euler differential equationThen the valu...
Let z = log x => x = e2
Put these values in given DE. we have,
Case -1 when 25 - 24λ > Qthen soln is given by,
Where c1 and c2 are arbitrary finite constants. Now we want when x → ∞ then y(x) -> 0 .
Now take
Now take
So in this case limit not exist.
So now no need to consider further case.
Now we can say no % exist for which all the soln tends to 0 as x → ∞
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Consider the 2nd order Cauchy-Euler differential equationThen the values of λfor which all the solutions of above DE tends to 0 asx →∞, isa)λ > 0b)λ≥ 1c)λ≥ 0d)No such λ existCorrect answer is option 'D'. Can you explain this answer?
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Consider the 2nd order Cauchy-Euler differential equationThen the values of λfor which all the solutions of above DE tends to 0 asx →∞, isa)λ > 0b)λ≥ 1c)λ≥ 0d)No such λ existCorrect answer is option 'D'. 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 Consider the 2nd order Cauchy-Euler differential equationThen the values of λfor which all the solutions of above DE tends to 0 asx →∞, isa)λ > 0b)λ≥ 1c)λ≥ 0d)No such λ existCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the 2nd order Cauchy-Euler differential equationThen the values of λfor which all the solutions of above DE tends to 0 asx →∞, isa)λ > 0b)λ≥ 1c)λ≥ 0d)No such λ existCorrect answer is option 'D'. Can you explain this answer?.
Consider the 2nd order Cauchy-Euler differential equationThen the values of λfor which all the solutions of above DE tends to 0 asx →∞, isa)λ > 0b)λ≥ 1c)λ≥ 0d)No such λ existCorrect answer is option 'D'. 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 Consider the 2nd order Cauchy-Euler differential equationThen the values of λfor which all the solutions of above DE tends to 0 asx →∞, isa)λ > 0b)λ≥ 1c)λ≥ 0d)No such λ existCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the 2nd order Cauchy-Euler differential equationThen the values of λfor which all the solutions of above DE tends to 0 asx →∞, isa)λ > 0b)λ≥ 1c)λ≥ 0d)No such λ existCorrect answer is option 'D'. Can you explain this answer?.
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