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    Nonhomogeneous Differential Equations : Particular and General Solutions

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    14. Consider the nonhomogeneous linear equation

    dy/dt = λy + cos(2t)

    To find its general solution, we add the general solution of the associated homogeneous equation and a particular solution
    yp(t) of the nonhomogeneous equation. Briefly explain why it does not matter which solution of the nonhomogeneous equation we use for yp(t).

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    Consider two different solutions of the nonhomogeneous equation, y_1(t) and y_2(t).
    Both of them satisfy the same differential equation:

    dy_1/dt = λy_1 + cos(2t) (1)

    dy_2/dt = ...

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