1. A differential equation is any equation which contains at  arbitrarydegreederivativedifferentialdifferential equationEuler’s homogeneityhighest order derivativehomogeneousintegrating a differential equationintegrationleast one derivative of an unknown functionorder of the differential equationordinaryOrdinary Differential EquationParticular Solutionprotonsradioactivesinglesolution of a differential equationunstable, either  arbitrarydegreederivativedifferentialdifferential equationEuler’s homogeneityhighest order derivativehomogeneousintegrating a differential equationintegrationleast one derivative of an unknown functionorder of the differential equationordinaryOrdinary Differential EquationParticular Solutionprotonsradioactivesinglesolution of a differential equationunstable derivative or partial  arbitrarydegreederivativedifferentialdifferential equationEuler’s homogeneityhighest order derivativehomogeneousintegrating a differential equationintegrationleast one derivative of an unknown functionorder of the differential equationordinaryOrdinary Differential EquationParticular Solutionprotonsradioactivesinglesolution of a differential equationunstable.

2.The order of a differential equation is the  arbitrarydegreederivativedifferentialdifferential equationEuler’s homogeneityhighest order derivativehomogeneousintegrating a differential equationintegrationleast one derivative of an unknown functionorder of the differential equationordinaryOrdinary Differential EquationParticular Solutionprotonsradioactivesinglesolution of a differential equationunstable present in the  arbitrarydegreederivativedifferentialdifferential equationEuler’s homogeneityhighest order derivativehomogeneousintegrating a differential equationintegrationleast one derivative of an unknown functionorder of the differential equationordinaryOrdinary Differential EquationParticular Solutionprotonsradioactivesinglesolution of a differential equationunstable.

3.If a differential equation is expressible in a polynomial form, then the integral power of thevhighest order derivative appears is called the  arbitrarydegreederivativedifferentialdifferential equationEuler’s homogeneityhighest order derivativehomogeneousintegrating a differential equationintegrationleast one derivative of an unknown functionorder of the differential equationordinaryOrdinary Differential EquationParticular Solutionprotonsradioactivesinglesolution of a differential equationunstable of the differential equation.

4.If a differential equation contains only ordinary derivatives of one or more functions with respect to a  arbitrarydegreederivativedifferentialdifferential equationEuler’s homogeneityhighest order derivativehomogeneousintegrating a differential equationintegrationleast one derivative of an unknown functionorder of the differential equationordinaryOrdinary Differential EquationParticular Solutionprotonsradioactivesinglesolution of a differential equationunstable independent variable, it is said to be an  arbitrarydegreederivativedifferentialdifferential equationEuler’s homogeneityhighest order derivativehomogeneousintegrating a differential equationintegrationleast one derivative of an unknown functionorder of the differential equationordinaryOrdinary Differential EquationParticular Solutionprotonsradioactivesinglesolution of a differential equationunstable (ODE).

5. “Solving a differential equation” is also referred to as “ arbitrarydegreederivativedifferentialdifferential equationEuler’s homogeneityhighest order derivativehomogeneousintegrating a differential equationintegrationleast one derivative of an unknown functionorder of the differential equationordinaryOrdinary Differential EquationParticular Solutionprotonsradioactivesinglesolution of a differential equationunstable”, since the process of finding the solution to a differential equation involves  arbitrarydegreederivativedifferentialdifferential equationEuler’s homogeneityhighest order derivativehomogeneousintegrating a differential equationintegrationleast one derivative of an unknown functionorder of the differential equationordinaryOrdinary Differential EquationParticular Solutionprotonsradioactivesinglesolution of a differential equationunstable.

6.A function f (x, y) is said to be a  arbitrarydegreederivativedifferentialdifferential equationEuler’s homogeneityhighest order derivativehomogeneousintegrating a differential equationintegrationleast one derivative of an unknown functionorder of the differential equationordinaryOrdinary Differential EquationParticular Solutionprotonsradioactivesinglesolution of a differential equationunstable function of degree n in the variables x and y if, f tx ty tn f x y ( , ) = ( , ) for some n∈¡ for all suitably restricted x, y and t . This is known as  arbitrarydegreederivativedifferentialdifferential equationEuler’s homogeneityhighest order derivativehomogeneousintegrating a differential equationintegrationleast one derivative of an unknown functionorder of the differential equationordinaryOrdinary Differential EquationParticular Solutionprotonsradioactivesinglesolution of a differential equationunstable.

7. The nucleus of an atom consists of combinations of  arbitrarydegreederivativedifferentialdifferential equationEuler’s homogeneityhighest order derivativehomogeneousintegrating a differential equationintegrationleast one derivative of an unknown functionorder of the differential equationordinaryOrdinary Differential EquationParticular Solutionprotonsradioactivesinglesolution of a differential equationunstable and neutrons. Many of these combinations of  arbitrarydegreederivativedifferentialdifferential equationEuler’s homogeneityhighest order derivativehomogeneousintegrating a differential equationintegrationleast one derivative of an unknown functionorder of the differential equationordinaryOrdinary Differential EquationParticular Solutionprotonsradioactivesinglesolution of a differential equationunstable and neutrons are  arbitrarydegreederivativedifferentialdifferential equationEuler’s homogeneityhighest order derivativehomogeneousintegrating a differential equationintegrationleast one derivative of an unknown functionorder of the differential equationordinaryOrdinary Differential EquationParticular Solutionprotonsradioactivesinglesolution of a differential equationunstable, that is the atoms decay or transmute into the atoms of another substance. Such nuclei are said to be  arbitrarydegreederivativedifferentialdifferential equationEuler’s homogeneityhighest order derivativehomogeneousintegrating a differential equationintegrationleast one derivative of an unknown functionorder of the differential equationordinaryOrdinary Differential EquationParticular Solutionprotonsradioactivesinglesolution of a differential equationunstable.

8. A  arbitrarydegreederivativedifferentialdifferential equationEuler’s homogeneityhighest order derivativehomogeneousintegrating a differential equationintegrationleast one derivative of an unknown functionorder of the differential equationordinaryOrdinary Differential EquationParticular Solutionprotonsradioactivesinglesolution of a differential equationunstable is an expression for the dependent variable in terms of the independent variable(s) which satisfies the  arbitrarydegreederivativedifferentialdifferential equationEuler’s homogeneityhighest order derivativehomogeneousintegrating a differential equationintegrationleast one derivative of an unknown functionorder of the differential equationordinaryOrdinary Differential EquationParticular Solutionprotonsradioactivesinglesolution of a differential equationunstable equation.

9. The solution which contains as many  arbitrarydegreederivativedifferentialdifferential equationEuler’s homogeneityhighest order derivativehomogeneousintegrating a differential equationintegrationleast one derivative of an unknown functionorder of the differential equationordinaryOrdinary Differential EquationParticular Solutionprotonsradioactivesinglesolution of a differential equationunstable constants as the  arbitrarydegreederivativedifferentialdifferential equationEuler’s homogeneityhighest order derivativehomogeneousintegrating a differential equationintegrationleast one derivative of an unknown functionorder of the differential equationordinaryOrdinary Differential EquationParticular Solutionprotonsradioactivesinglesolution of a differential equationunstable is called the general solution.

10. If we give particular values to the arbitrary constants in the general solution of differential equation, the resulting solution is called a  arbitrarydegreederivativedifferentialdifferential equationEuler’s homogeneityhighest order derivativehomogeneousintegrating a differential equationintegrationleast one derivative of an unknown functionorder of the differential equationordinaryOrdinary Differential EquationParticular Solutionprotonsradioactivesinglesolution of a differential equationunstable.