DIFFERENTIAL EQUATIONS

DIFFERENTIAL EQUATIONS

1. Notations

2. A differential equation is an equation that contains one or more functions with its derivatives.

   • Order
     • It is the order of the highest derivative (also known as differential coefficient) present in the equation.
   • Linearity
     • A differential equation is linear if the dependent variable and all its derivatives appear in a linear fashion (i.e., they are not multiplied together or squared for example or they are not part of transcendental functions such as sins, cosines, exponentials, etc.).
   • Degree
     • The degree of the differential equation is represented by the power of the highest order derivative in the given differential equation.

3. Types of solutions

   • Particular solution • Represents a specific solution of the differential equation.
   • General solution • Represents a family of functions that satisfy the differential equation.