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The value of α is_________ , where α ∈ R ,s.t the differential equation , y" + 2(α-1)(α-3)y' + (α-2)y = 0,has a solution y(x) = a cos(αx) + b sin(βx) for some non-zero real no's a,b.
    Correct answer is '3'. Can you explain this answer?
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    The value of α is_________ , where α ∈ R ,s.t the dif...
    here given eqn is,
    here the soln of this eqn is given by we know that differential equation will have such solution only when AE has complex root, whose real part is zero.
    thus in equation (1), (α-1)(α-3) = 0 => a = 1,3
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    The value of α is_________ , where α ∈ R ,s.t the dif...
    Explanation:

    Given Differential Equation:
    The given differential equation is y'' + 2(α-1)(α-3)y + (α-2)y = 0.

    Assumed Solution:
    Let the solution be y(x) = a cos(αx) + b sin(βx) for some non-zero real numbers a, b.

    Substitute the Assumed Solution:
    Substitute the assumed solution into the differential equation and simplify the terms.

    Identify the Coefficients:
    Compare the coefficients of cos(αx) and sin(βx) terms to find the values of α and β.

    Obtain the Value of α:
    By equating the coefficients of cos(αx) and sin(βx) terms, we get α = 3 as the value that satisfies the given conditions.

    Conclusion:
    Therefore, the value of α is 3, which satisfies the given differential equation and allows for a solution in the form y(x) = a cos(3x) + b sin(βx) for some non-zero real numbers a, b.
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    The value of α is_________ , where α ∈ R ,s.t the dif...
    here given eqn is,
    here the soln of this eqn is given by we know that differential equation will have such solution only when AE has complex root, whose real part is zero.
    thus in equation (1), (α-1)(α-3) = 0 => a = 1,3
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    The value of α is_________ , where α ∈ R ,s.t the differential equation , y" + 2(α-1)(α-3)y + (α-2)y = 0,has a solution y(x) = a cos(αx) + b sin(βx) for some non-zero real nos a,b.Correct answer is '3'. Can you explain this answer?
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    The value of α is_________ , where α ∈ R ,s.t the differential equation , y" + 2(α-1)(α-3)y + (α-2)y = 0,has a solution y(x) = a cos(αx) + b sin(βx) for some non-zero real nos a,b.Correct answer is '3'. 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 The value of α is_________ , where α ∈ R ,s.t the differential equation , y" + 2(α-1)(α-3)y + (α-2)y = 0,has a solution y(x) = a cos(αx) + b sin(βx) for some non-zero real nos a,b.Correct answer is '3'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The value of α is_________ , where α ∈ R ,s.t the differential equation , y" + 2(α-1)(α-3)y + (α-2)y = 0,has a solution y(x) = a cos(αx) + b sin(βx) for some non-zero real nos a,b.Correct answer is '3'. Can you explain this answer?.
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