I wonder why "to" is utilized in the following sentence rather than "for"
This chapter is devoted 'to' solving ordinary differential equations of the form
In my understanding if "to" is used, then the "ing" prefix should not be added to "solve".
The verb devote takes the preposition "to" after it, not for. Just as we use the -ing form of a verb after the phrasal verb 'look forward', we always use a noun phrase or the -ing form of a verb after the phrase devote to/devoted to, as commented by Damkerng T.
She devoted her life to serving the sick.
She's devoted to serving the sick.
This chapter is devoted to politics.
So the sentence "This chapter is devoted to solving ordinary......" is correct grammatically.
I prefer to think of it this way:
"to" is used when the object of the sentence is a target or goal. Whereas "for" is used when the object of the sentence is an intended recipient of something, or a customer.
In this case, "solving ordinary differential equations of the form" is more of a goal than anything else within those cases, so "to" is used.