General Solutions (Edexcel A Level Maths): Revision Note

General Solutions

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