Differential Equations

Basic Concepts (Differential Equations)


  • We shall prefer to use the following notations for derivatives:
    \frac{dy}{dx}=y',\frac{d^2y}{dx^2}=y'',\frac{d^3y}{dx^3}=y'''
  • An equation involving derivatives of the dependent variable with respect to independent variable (variables) is known as a differential equation.
  • Order of a differential equation is the order of the highest order derivative occurring in the differential equation.
  • Degree of a differential equation is defined if it is a polynomial equation if its derivatives.
  • Degree (when defined) of a differential equation is the highest power (positive integer only) of the highest order derivative in it.
  • Order and degree (if defined) of a differential equation are always positive integers.

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  •  For derivatives of higher order, it will be inconvenient to use so many dashes as supersuffix therefore, we use the notation yn for nth order derivative \frac{d^ny}{dx^n}.