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Nonhomogeneous Differential Equations : Particular and General Solutions

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).


Solution Preview

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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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.