鼓励 vs. 鼓舞
gǔlì vs. gǔwǔ

Both words mean “to inspire, to encourage.”

1. 鼓励, as a verb, usually has a person for its subject, while the subject of 鼓舞 is usually an incident.
(1) 他鼓励我继续学习钢琴。
tā gǔ lì wǒ jì xù xué xí gāng qín
He encouraged me to keep learning to play the piano.

(2) 每当我失败的时候，妈妈总是鼓励我重新开始。
Měi dāng wǒ shī bài de shí hòu, mā mā zǒng shì gǔ lì wǒ chóng xīn kāi shǐ.
My mother encourages me to pull myself together when I fail.

(3) 将军的话鼓舞了战士们的士气。
Jiāng jūn de huà gǔ wǔ le zhàn shì men de shì qì.
The general's speech boosted the troops' morale.

(4) 虽然只是一次小小的胜利，却大大地鼓舞了我们。
Suī rán zhī shì yí cì xiǎo xiǎo de shèng lì, què dà dà de gǔ wǔ le wǒ men.
Although this is just a small victory, it raised our spirits.

2. The incident that encourages a person is usually positive and the result is positive too. But 鼓励 can be used in a negative case.
(1) 监考的时候睁一只眼闭一只眼，不就等于鼓励大家作弊吗？
Jiānkǎo de shí hòu zhēng yì zhī yǎn bì yì zhī yǎn, bù jiù děng yú gǔ lì dà jiā zuò bì ma.
A half-hearted test minder may give the students a chance to cheat.

这两个词都可以表示使人振作，催人奋进。 先看动词用法。
1. “鼓励” (动) 的施行者常是人，“舞” (动) 的施行者常常是事件。
2. “鼓舞” 人的事件一般是积极性的，结果也是积极的，“鼓励” 有时候可以是消极的。