General Solutions (Edexcel International A Level (IAL) Maths) : Revision Note
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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
Worked Example

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