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