Application of Differential Equation





Application of Differential Equation

 

Differential equation can be defined as a mathematical equation for an unknown function of one or more variables and the Variables are related to the value of the function itself and its derivation of various order. Differential equation plays an important role in the field of math, physics, engineering etc.

 

Some useful relations:

  1. Slope of tangent = \dfrac{dy}{dx}
  2. Slope of normal = - \dfrac{dx}{dy}
  3. Length of tangent = \dfrac{y}{\left(\frac{dy}{dx} \right)^2} \sqrt{1 + \left(\dfrac{dy}{dx} \right)^2}
  4. Length of normal = y \sqrt{1 + \left( \dfrac{dy}{dx} \right)^2}
  5. Equation of tangent at p (x_1, y_1) is Y- y_1 = \dfrac{dy}{dx} (X- x_1)
  6. Equation of Normal Y- y_1 = \dfrac{dx}{dy} (X- x_1)
  7. Radius of curvature\rho = \dfrac{\{1 + \left(\dfrac{dy}{dx} \right)^2 \}^\frac{3}{2}}{\dfrac{d^2y}{dx^2}} or \rho = \dfrac{ds}{d\Psi}

 

 



Related posts:

  1. Formulas for Parabola Formulas for Parabola   Parabola is a Greek word which...
  2. Derivative Formula Derivative Formulas Derivative is a rate of change of function...
  3. Co-ordinate Geometry Formulas Co-ordinate Geometry Formulas co-ordinate geometry is one of the most...
  4. Derivative or Differential Coefficient of a Function. Differential calculus or the concept of Derivative and Differential Coefficient...
  5. Derivatives of Trigonometric functions. As you know, The functions SINE x(sin x) , CO-SECANT...