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What is a differential equation?

I'm in year 12 (doing AS maths and FM, Edexcel) and I hear year 13's talking about how you do partial differential equations in C4 and first and second order differential equations in FP2 and I was wondering...
What are they? What makes them different to a polynomial equation?

Reply 1

username2130115

a differential equation is an equation which involves the derivatives of a function. polynomials do not always involve derivatives. e.g. f'(x) = f(x) - 2x - 2. these types of differential equations are not partial differential equations because they only have one variable x; they are correctly known as 'ordinary differential equations'.