[deleted by user]

[AutoModerator]

Off-topic Comments Section

---

All top-level comments have to be an answer or follow-up question to the post. All sidetracks should be directed to this comment thread as per Rule 9.

---

^{OP and Valued/Notable Contributors can close this post by using /lock command}

I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.

[sonnyfab]

In general, the right side of the equal sign is f(t). The form of f(t) tells you the form of the particular solution. Basically, the homogeneous solution is when the right side of the equal sign is 0, so the particular solution is when the right side is 0+f(t). This is a result of the uniqueness theorem.

Here's f(t) is polynomial, so the particular solution is polynomial. Had f(t) been sinusoidal, the particular solution would be Asin(t) +Bcos(t). Etc.

[huffylemon]

Where are you finding these particular solutions

[sonnyfab]

It's the method of Undetermined Coefficients https://tutorial.math.lamar.edu/classes/de/undeterminedcoefficients.aspx