You can use boundary conditions to find a particular solution when solving a second order linear differential equation as this video demonstrates.

Solve

  1. \dfrac{{{d^2}y}}{{d{x^2}}} - 3\dfrac{{dy}}{{dx}} + 2y = 4 + x \text{    given  }y = 4 \text{,  }\dfrac{{dy}}{{dx}} = 2 \text{    when  }x = 0
2nd Order Linear Differential Equations : Particular Solutions : ExamSolutions - youtube Video