Then the donkey starts purposely falling into the water every day.

首先,start后面确实是接to do 和ing都可以
虽然两者有时候可以通用
但是两者还是有区别的
start to do
start doing
1) 谈及一项长期活动或开始一种习惯时,使用doing.
How old were you when you first started playing the piano?你几岁时开始弹钢琴?
2) begin,start用进行时时,后面动词用不定式to do
I was beginning to get angry.我开始生起气来.
3) 在 begin,start 后接know,understand,realize这类动词时,常用不定式to do
I begin to understand the truth.我开始明白真相.
4) 物作主语时
It began to melt.
一般情况下没区别
只有三种情况只用start to do sth.
1.start本身用-ing
He is just starting to write the letter.
2.主语是物不是人
The ice started to melt.
3.其后的动词与想法\感情有关
She started to understand it.
我是coldinkaren.希望可以帮到你,有不懂的还可以问我^^