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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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Nonhomogeneous Differential Equations, Particular and General Solutions are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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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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