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If the Particular Integral (P.I.) of the differential equation (D3 + 1)y = cos2x. is given by y = 1/65 (cos 2x - β sin 2x). Find the value of β
    Correct answer is '-0.123'. Can you explain this answer?
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    If the Particular Integral (P.I.) of the differential equation (D3 + 1...



    The correct answer is: -0.123
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    If the Particular Integral (P.I.) of the differential equation (D3 + 1...
    Sin 2x), what is the general solution of the differential equation?

    The general solution of a differential equation is the sum of the homogeneous solution and the particular integral.

    The homogeneous solution of the differential equation (D^3 - 1)y = 0 can be found by assuming a solution of the form y = e^(mx), where m is a constant. Substituting this into the differential equation, we get (D^3 - 1)e^(mx) = 0. This simplifies to m^3e^(mx) - e^(mx) = 0. Factoring out e^(mx), we have e^(mx)(m^3 - 1) = 0. This equation holds if either e^(mx) = 0 (which is not possible) or m^3 - 1 = 0. Solving for m, we find m = 1, -1/2 + sqrt(3)/2, -1/2 - sqrt(3)/2.

    Therefore, the homogeneous solution is y_h = C1e^x + C2e^((-1/2 + sqrt(3)/2)x) + C3e^((-1/2 - sqrt(3)/2)x), where C1, C2, and C3 are arbitrary constants.

    The general solution of the differential equation is y = y_h + y_p. Substituting the given particular integral, we have y = C1e^x + C2e^((-1/2 + sqrt(3)/2)x) + C3e^((-1/2 - sqrt(3)/2)x) + 1/65 (cos 2x - sin 2x).
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    If the Particular Integral (P.I.) of the differential equation (D3 + 1)y = cos2x.is given by y = 1/65 (cos 2x -β sin 2x).Find the value ofβCorrect answer is '-0.123'. Can you explain this answer?
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    If the Particular Integral (P.I.) of the differential equation (D3 + 1)y = cos2x.is given by y = 1/65 (cos 2x -β sin 2x).Find the value ofβCorrect answer is '-0.123'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about If the Particular Integral (P.I.) of the differential equation (D3 + 1)y = cos2x.is given by y = 1/65 (cos 2x -β sin 2x).Find the value ofβCorrect answer is '-0.123'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the Particular Integral (P.I.) of the differential equation (D3 + 1)y = cos2x.is given by y = 1/65 (cos 2x -β sin 2x).Find the value ofβCorrect answer is '-0.123'. Can you explain this answer?.
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