I want to write a question in Math. as below but I don't know the difference between them:
Determine the solution of the differential equation?
Find the solution of the differential equation?
Determine means to evaluate evidence and come to a conclusion or judgement, or to gather information about a fact or state of something.
Find can mean this (especially in a legal context), but find can also mean simply "to search for the location of" - and determine won't ever mean that.
But it's possible to "determine" the state or location of things, but you do need to specify the attribute you are determining, whereas with find X it's implied you are trying to determine where X is located.
A contrived example to illustrate:
I lost my keys. I can't find them. (Find implies "where")
I lost my keys. I can't determine them. (Wrong - sounds like there is a second object and you can't tell whether or not it's keys - and not necessarily your keys)
I lost my keys. I can't determine the location of them. (We specify "location" as an attribute we want to discover, so this is OK, but a little over wordy)
In maths both work. You'll often see many sentences involving those words.
» Determine/find all the continuous functions that satisfy...
» Determine/find the nilpotent matrix which commutes...
» Determine/find the value of the following integral and...
They naturally work with any math sentence.
In exams or any kind of evaluation, both words are prefered.