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Differential equations

There are many notations for differential equations in mathematics. Some of them are strict, but the others leads to ambiguity.

y'' + y = x

This equation may be equal to the following, in which x is an argument of y:

y''(x) + y(x) = x

But the equation may be also equal to the next equation, in which x is a parameter:

y''(t) + y(t) = x

Uniquation supports both form, but it's better to use the last one to avoid the ambiguity.

As it is seem on example above to turn a function into a derivative it is enough to place ' between the function and the argument. If a derivative of function has argument all the others includes of the function into formula must be with argument too, for example formulas 'y''(t) + y(t) = 0' and 'y'' + y = 0' are correct, but 'y''(t) + y = 0' isn't.

Enter the following formula in TeX to check yourself: