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Let L(y) = yn+ a1y'+a2y where a1, a2 are constants, and Let p(r) denote its characterstic polynomial. Then which of the following is/are correct?
  • a)
    If A. α are constants and P(α)≠ 0. then Φ(x) = Beax, where B is constant is solution of L(y) = Aeax.
  • b)
    If Φ(x) and Ψ (x) are solutions of L(y) = b1(x) and L(y) = b2 (x), then Φ(x) + Ψ (x) is solutionof L(y) = b1 (x) + b2 (x).
  • c)
    If a1 = 0 and a2 = ω2, where ω is +ve constant, then every solution Φ(x) of L(y) = A cos ωx approaches to infinity for large value of x.
  • d)
    None of these
Correct answer is option 'A,B,C'. Can you explain this answer?
Most Upvoted Answer
Let L(y) = yn+ a1y+a2y where a1, a2are constants, and Let p(r) denote ...
L(y) = y" + a1 : y' + a2y
If p(α) = 0 then Φ(x) = Beax is a soution of L(y) = 0
If p(α ) ≠ 0 then Φ(x) = Beax gives L(y) = Aeax where A = B (α2 + a1, α + a,2)
Option (a) is correct.
Given Φ" + a1 Φ' + a2 ·Φ = b1            .....(1)
and Ψ" + a1 ·Ψ' + a2Ψ = b2                 .....(2)
then (Φ+Ψ)'' +a1 (Φ+Ψ)' + a,2(Φ+Ψ) = b1 + b2
⇒ Φ(x) + Ψ (x) is a solution of L(y) = b1(x) + b2(x)
Option (b) is true
For a1 = 0. a2 = w2
y" + w2y = 0
⇒ y(x) = c1cos (wx) + c2sin (wx)
Now, 
General solution of L(y) = Acos (wx) is y(x) = 
Option (c) is correct
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Let L(y) = yn+ a1y+a2y where a1, a2are constants, and Let p(r) denote its characterstic polynomial.Then which of the following is/are correct?a)If A.α are constants and P(α)≠0. then Φ(x) = Beax, where B is constant is solution of L(y) = Aeax.b)If Φ(x) and Ψ (x) are solutions of L(y) = b1(x) and L(y) = b2(x), then Φ(x) + Ψ (x) is solutionof L(y) = b1(x) + b2(x).c)If a1= 0 and a2=ω2, whereωis +ve constant, then every solution Φ(x) of L(y) = A cosωx approaches to infinity for large value of x.d)None of theseCorrect answer is option 'A,B,C'. Can you explain this answer?
Question Description
Let L(y) = yn+ a1y+a2y where a1, a2are constants, and Let p(r) denote its characterstic polynomial.Then which of the following is/are correct?a)If A.α are constants and P(α)≠0. then Φ(x) = Beax, where B is constant is solution of L(y) = Aeax.b)If Φ(x) and Ψ (x) are solutions of L(y) = b1(x) and L(y) = b2(x), then Φ(x) + Ψ (x) is solutionof L(y) = b1(x) + b2(x).c)If a1= 0 and a2=ω2, whereωis +ve constant, then every solution Φ(x) of L(y) = A cosωx approaches to infinity for large value of x.d)None of theseCorrect answer is option 'A,B,C'. 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 Let L(y) = yn+ a1y+a2y where a1, a2are constants, and Let p(r) denote its characterstic polynomial.Then which of the following is/are correct?a)If A.α are constants and P(α)≠0. then Φ(x) = Beax, where B is constant is solution of L(y) = Aeax.b)If Φ(x) and Ψ (x) are solutions of L(y) = b1(x) and L(y) = b2(x), then Φ(x) + Ψ (x) is solutionof L(y) = b1(x) + b2(x).c)If a1= 0 and a2=ω2, whereωis +ve constant, then every solution Φ(x) of L(y) = A cosωx approaches to infinity for large value of x.d)None of theseCorrect answer is option 'A,B,C'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let L(y) = yn+ a1y+a2y where a1, a2are constants, and Let p(r) denote its characterstic polynomial.Then which of the following is/are correct?a)If A.α are constants and P(α)≠0. then Φ(x) = Beax, where B is constant is solution of L(y) = Aeax.b)If Φ(x) and Ψ (x) are solutions of L(y) = b1(x) and L(y) = b2(x), then Φ(x) + Ψ (x) is solutionof L(y) = b1(x) + b2(x).c)If a1= 0 and a2=ω2, whereωis +ve constant, then every solution Φ(x) of L(y) = A cosωx approaches to infinity for large value of x.d)None of theseCorrect answer is option 'A,B,C'. Can you explain this answer?.
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