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If the Particular Integral (PI) of the Differential equation (D2 + a2)y = cos ax is given by f(x). Then find the value of a2f (π/2a).
    Correct answer is '0.785'. Can you explain this answer?
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    If the Particular Integral (PI) of the Differential equation(D2+a2)y= ...
    As, we known, the P.I. of (D2 + a2)y = cos ax is given as  x/2a sin ax
    ∴  
    Now,  

    The correct answer is: 0.785
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    If the Particular Integral (PI) of the Differential equation(D2+a2)y= ...
    To find the particular integral of the differential equation, we can assume a particular solution of the form f(x) = A cos(ax) + B sin(ax), where A and B are constants to be determined.

    Taking the second derivative of f(x) with respect to x, we have:
    f''(x) = -A a^2 cos(ax) - B a^2 sin(ax)

    Substituting this into the differential equation, we get:
    (-A a^2 cos(ax) - B a^2 sin(ax)) + a^2 (A cos(ax) + B sin(ax)) = cos(ax)

    Simplifying this equation, we have:
    (-A a^2 + a^2 A) cos(ax) + (-B a^2 + a^2 B) sin(ax) = cos(ax)

    Since cos(ax) and sin(ax) are linearly independent, the coefficients of cos(ax) and sin(ax) must be equal on both sides of the equation. Therefore,
    -A a^2 + a^2 A = 1 (1)
    -B a^2 + a^2 B = 0 (2)

    From equation (2), we have -Ba^2 + a^2 B = 0, which implies B = 0.

    Substituting B = 0 into equation (1), we have -A a^2 + a^2 A = 1, which simplifies to A = -1.

    Therefore, the particular solution f(x) is given by:
    f(x) = -cos(ax)

    To find the value of a^2 f(x), we substitute f(x) = -cos(ax) into the expression:
    a^2 f(x) = a^2 (-cos(ax)) = -a^2 cos(ax)

    So, the value of a^2 f(x) is -a^2 cos(ax).
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    If the Particular Integral (PI) of the Differential equation(D2+a2)y= ...
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    If the Particular Integral (PI) of the Differential equation(D2+a2)y= cosaxis given byf(x).Then find the value of a2f (π/2a).Correct answer is '0.785'. Can you explain this answer?
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