Both Uses

resolve
in
Jacob Have I Loved
(Edited)

But as fast as I would repent, resolving never again to hate, some demon would slip into my soul, tug at the corner, and...
Chpt 6 *

resolving = definitely deciding
"The only way to resolve the problem of the cats," he said, "is to dispose of them humanely."
Chpt 9 *

resolve = solve or settle

Definitions:

(1) (resolve as in: I resolved to stop drinking.)
to decide -- typically a firm or formal decision

In modern writing resolve is typically used to emphasize a firm or formal decision. In classic literature, it is used more frequently and often simply replaces decide or determine.
(2) (resolve as in: This committee hereby resolves...)
make a decision or voice an opinion by formal group vote
(3) (resolve as in: Her resolve weakened.)
firmness of purpose (strong determination to do something)
(4) (resolve as in: How was the problem resolved?)
to solve a problem, settle a disagreement, or for a situation to change
(5) (meaning too rare to warrant focus)
Less commonly, resolve can mean:
- to make clearly visible -- as in "The microscope cannot resolve that level of detail."
- to divide into parts -- as in "The problem resolves into three parts,"or (math) "Resolve the polynomial into factors," or (chemistry) "As the temperature changes, the compound resolves into its component parts," or (physics) "The force on the inclined plane resolves into horizontal and vertical components."
- reduce or convert into something else -- as in "The URL is resolved to an IP address," or (music) "The progression is resolved as the dissonance is replaced by consonance."