Differential Equations

§ Ordinary Differential Equation: A differential equation involving derivatives with respect to a single independent variable is known as ordinary differential equation.

§ Partial Differential Equation: A differential equation involving partial derivation with respect to more than one independent variable is known as partial differential equation.

§ Linear differential equation: A differential equation is called linear if,

(i) Every dependent variables and every derivatives involved should be in first degree only and

(ii) No product of dependent variables and/or derivative occurs.

§ A differential equation which is not linear is known as non-linear differential equation.

• Standard Form of differential equation: An equation involving one or more derivatives is called derivative standard form for a first order differential equation in the unknown function y(x) is f(x,y)= dy/dx.

• Order of a Differential Equation: The order of the highest derivative involved in a differential equation is called the order of the differential equation.

• Degree of a Differential Equation: The degree of a differential equation is the exponent of the highest derivative which occurs in it after making the derivatives free for radicals and fractions.

• Solution of differential equation:

  (1) General Solution: The solution of the differential equation contains arbitrary constant equals the degree of differential equation.

  (2)