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Differential Equations of First Order and First Degree

  1. An equation that involves independent and dependent variables and the derivatives of the dependent variable w.r.t. independent variable is called a differential equation.
    102289.png dy = sin x dx, 102283.png etc.
  2. A differential equation is said to be ordinary, if the differential coefficients have reference to a single independent variable only and it is said to be partial if there are two or more independent variables. We are concerned with ordinary differential equations only.
    For example,
    102277.png + 2y = 0
    is ordinary differential equation
    102271.png = 0; 102265.png = x2 + y
    are partial differential equation.

Order and degree of differential equations

The order of a differential equation is the order of the highest differential coefficient occurring in it.
The degree of a differential equation which is expressed or can be expressed as a polynomial in the derivatives is the degree of the highest order derivative occurring in it, after it has been expressed in a form free from radicals and fractions as far as derivatives are concerned, thus the differential equation:
f(x, y) 102258.png + φ (x, y) 102252.png + ... = 0 is of order m and degree p.

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