# 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).

https://brainmass.com/math/partial-differential-equations/nonhomogeneous-differential-equations-particular-general-145384

#### 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 = ...

#### Solution Summary

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.