What is a particular solution?

• Ensure you are familiar with?General?Solutions?first
• With extra information, the constant of integration,?c, can be found
• This means the?particular?solution?(from the family of solutions) can be found

What is a boundary condition/initial condition?

• A?boundary condition?is a piece of extra information that lets you find the particular solution
  • For example knowing?y = 4?when?x = 0?in the preceding example
  • In a model this could be a particle coming to rest after a certain time, ie?v = 0?at time?t

• Differential equations are used in modelling, experiments and real-life situations
• A boundary condition is often called an?initial?condition?when it gives the situation at the start of the model or experiment
  • This is often linked to time, so?t = 0

• It is possible to have two boundary conditions
  • eg a particle initially at rest has velocity,?v = 0?and acceleration,?a = 0?at time,?t = 0
  • for a?second order?differential equation you need?two?boundary conditions to find the particular solution