What is a differential equation?
- Any equation, involving a derivative term, is a differential equation
- Equations involving only first derivative terms are called first order differential equations
- Equations involving second derivative terms are called second order differential equations
What is a general solution?
- Integration will be involved in solving the differential equation
- ie working back to “y = f(x)”
- A constant of integration, c is produced
- This gives an infinite number of solutions to the differential equation, each of the form y = g(x) + c (ie y = f(x) where f(x) = g(x) + c)
- These are often called a family of solutions …
- … and the solution y= g(x) + c is called the general solution