Introduction

Introduction #

If the order of the differential equation is n, then n arbitrary constants will appear in the solution

Types of solutions:

• General solution: It is that solution where no. of arbitrary constants = order of differential equation
  • Also called complete integral or complete primitive of the differential equation.
• Particular solution: It is that which can be obtained from the general solution by giving particular values to the arbitrary constants.
• Singular solution: The singular solution is that solution which can’t be obtained from general solution.

Example #

$$ \begin{align*} D.E.=(y’)^2+xy’=y\\ General\\ solution:\\ y=cx^2+c^2\\ Singular\\ solution:\\ 4y+x^2=0 \end{align*} $$