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Math Help - Second Order Differential Equation

  1. #1
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    Second Order Differential Equation

    how to solve the second order differential equation in the form:
    ay" + by' + cy = R(x)?

    the example is this:
    (d2i/dt2) + 6(di/dt) +25i = -292sin(4t)
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  2. #2
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    Quote Originally Posted by sweetadam View Post
    how to solve the second order differential equation in the form:
    ay" + by' + cy = R(x)?

    the example is this:
    (d2i/dt2) + 6(di/dt) +25i = -292sin(4t)
    First you find the general solution of the corresponding homogeneous equations ie. ay'' + by' + cy = 0.

    Then you look for a particular solution, since in this case g(t) = -292\sin{4t} we can guess that the particular solution will be of the form Y(t) = A\cos{4t} + B\sin{4t}. Now you solve for A and B obviously, by substituting in the appropriate terms ie. y'' and y' and y into your original differential equation. Then you know the general form of the solution of nonhomogeneous equation is simply y = \phi(t) = c_1y_1(t) + c_2y_2(t) + Y(t), where y_1(t) and y_2(t) are solutions of the homogeneous equation and Y(t) is the particular solution we guessed and solved the constants A and B for. And c_1 and c_2 are arbitrary constants.
    Thanks from sweetadam
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