Mathematics Exam  >  Mathematics Questions  >  Suppose that L(y) = y + a1y + a2y = b(x), whe... Start Learning for Free
Suppose that L(y) = y'' + a1y' + a2y = b(x), where a1, a2 are constants and b(x) is a continuous function on  Then consider the statements
I. If b(x) is bounded on [0, ∞), then every solution of L(y) = b(x) is bounded on [0, ∞).
II. If b(x) → 0 as x → ∞, then every solution of L(y) = b(x) tends too as x → ∞.
  • a)
     only I is correct
  • b)
     only II is correct
  • c)
     Both are correct
  • d)
     Neither of them is correct
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Suppose that L(y) = y + a1y + a2y = b(x), where a1, a2 are constants a...
y" -2y' + y = e-x
Where a1 = -2, a2 = 1 are constants and b (x) = e-x is a continuous function an [0,∞)
Now, y(x) = ex + xex +1/4e-x is one of the solutions of given ODE
Since b(x) =e-x is bounded on [0,∞)
but y(x) is unbounded on [0,∞) because 
Both statement are false
Explore Courses for Mathematics exam
Suppose that L(y) = y + a1y + a2y = b(x), where a1, a2 are constants and b(x) is a continuous function onThen consider the statementsI. If b(x) is bounded on [0, ∞), then every solution of L(y) = b(x) is bounded on [0, ∞).II. If b(x) → 0 as x → ∞, then every solution of L(y) = b(x) tends too as x → ∞.a)only I is correctb)only II is correctc)Both are correctd)Neither of them is correctCorrect answer is option 'D'. Can you explain this answer?
Question Description
Suppose that L(y) = y + a1y + a2y = b(x), where a1, a2 are constants and b(x) is a continuous function onThen consider the statementsI. If b(x) is bounded on [0, ∞), then every solution of L(y) = b(x) is bounded on [0, ∞).II. If b(x) → 0 as x → ∞, then every solution of L(y) = b(x) tends too as x → ∞.a)only I is correctb)only II is correctc)Both are correctd)Neither of them is correctCorrect 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 Suppose that L(y) = y + a1y + a2y = b(x), where a1, a2 are constants and b(x) is a continuous function onThen consider the statementsI. If b(x) is bounded on [0, ∞), then every solution of L(y) = b(x) is bounded on [0, ∞).II. If b(x) → 0 as x → ∞, then every solution of L(y) = b(x) tends too as x → ∞.a)only I is correctb)only II is correctc)Both are correctd)Neither of them is correctCorrect 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 Suppose that L(y) = y + a1y + a2y = b(x), where a1, a2 are constants and b(x) is a continuous function onThen consider the statementsI. If b(x) is bounded on [0, ∞), then every solution of L(y) = b(x) is bounded on [0, ∞).II. If b(x) → 0 as x → ∞, then every solution of L(y) = b(x) tends too as x → ∞.a)only I is correctb)only II is correctc)Both are correctd)Neither of them is correctCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Suppose that L(y) = y + a1y + a2y = b(x), where a1, a2 are constants and b(x) is a continuous function onThen consider the statementsI. If b(x) is bounded on [0, ∞), then every solution of L(y) = b(x) is bounded on [0, ∞).II. If b(x) → 0 as x → ∞, then every solution of L(y) = b(x) tends too as x → ∞.a)only I is correctb)only II is correctc)Both are correctd)Neither of them is correctCorrect answer is option 'D'. 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 Suppose that L(y) = y + a1y + a2y = b(x), where a1, a2 are constants and b(x) is a continuous function onThen consider the statementsI. If b(x) is bounded on [0, ∞), then every solution of L(y) = b(x) is bounded on [0, ∞).II. If b(x) → 0 as x → ∞, then every solution of L(y) = b(x) tends too as x → ∞.a)only I is correctb)only II is correctc)Both are correctd)Neither of them is correctCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Suppose that L(y) = y + a1y + a2y = b(x), where a1, a2 are constants and b(x) is a continuous function onThen consider the statementsI. If b(x) is bounded on [0, ∞), then every solution of L(y) = b(x) is bounded on [0, ∞).II. If b(x) → 0 as x → ∞, then every solution of L(y) = b(x) tends too as x → ∞.a)only I is correctb)only II is correctc)Both are correctd)Neither of them is correctCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Suppose that L(y) = y + a1y + a2y = b(x), where a1, a2 are constants and b(x) is a continuous function onThen consider the statementsI. If b(x) is bounded on [0, ∞), then every solution of L(y) = b(x) is bounded on [0, ∞).II. If b(x) → 0 as x → ∞, then every solution of L(y) = b(x) tends too as x → ∞.a)only I is correctb)only II is correctc)Both are correctd)Neither of them is correctCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Suppose that L(y) = y + a1y + a2y = b(x), where a1, a2 are constants and b(x) is a continuous function onThen consider the statementsI. If b(x) is bounded on [0, ∞), then every solution of L(y) = b(x) is bounded on [0, ∞).II. If b(x) → 0 as x → ∞, then every solution of L(y) = b(x) tends too as x → ∞.a)only I is correctb)only II is correctc)Both are correctd)Neither of them is correctCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Suppose that L(y) = y + a1y + a2y = b(x), where a1, a2 are constants and b(x) is a continuous function onThen consider the statementsI. If b(x) is bounded on [0, ∞), then every solution of L(y) = b(x) is bounded on [0, ∞).II. If b(x) → 0 as x → ∞, then every solution of L(y) = b(x) tends too as x → ∞.a)only I is correctb)only II is correctc)Both are correctd)Neither of them is correctCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Mathematics tests.
Explore Courses for Mathematics exam
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev