First Order Differential Equations
What is a differential equation?
- A differential equation is simply an equation that contains derivatives
- For example is a differential equation
- And so is
What is a first order differential equation?
- A first order differential equation is a differential equation that contains first derivatives but no second (or higher) derivatives
- For example is a first order differential equation
- But is not a first order differential equation, because it contains the second derivative
- The general solution to a first order differential equation will have one unknown constant
- To find the particular solution you will need to know an initial condition or a boundary condition
Wait – haven’t I seen first order differential equations before?
- Yes you have!
- For example is also a first order differential equation, because it contains a first derivative and no second (or higher) derivatives
- But for that equation you can just integrate to find the solution y = x3 + c (where c is a constant of integration)
- In A Level Maths you will have solved some first order differential equations using the method of separation of variables