**1.**- A
**differential equation**is an equation involving an unknown function and its derivatives. **2.**- The
**order**of the differential equation is the order of the highest derivative of the unknown function involved in the equation. **3.**- A
**linear differential equation**of order*n*is a differential equation written in the following form:where is not the zero function. Note that some may use the notation for the derivatives.

A linear equation obliges the unknown function*y*to have some restrictions. Indeed, the only operations which are accepted for the variable*y*are:**(i)**- Differentiating
*y*; **(ii)**- Multiplying
*y*and its derivatives by a function of the variable*x* **(iii)**- Adding what you obtained in (ii) and let it be equal to a
function of
*x*.

**4.**-
**Existence**: Does a differential equation have a solution? **5.**-
**Uniqueness**: Does a differential equation have more than one solution? If yes, how can we find a solution which satisfies particular conditions? **6.**- A problem in which we are looking for the unknown function
of a differential equation where the values of the unknown function
and its derivatives at some point are known is called an
**initial value problem**(in short IVP). **7.**- If no initial conditions are given, we call the description of all
solutions to
the differential equation the
**general solution**.

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