Question

How do you know if a differential equation is linear?

Answer 1

A linear differential equation is one in which the dependent variable only appears with an exponent of 0 or 1. (Note that the independent variable can appear raised to any power or as the argument of any function); it's only the exponent of the dependent variable that counts.

For instance, for y as a function of x, the "ugly" differential equation:

cos(x)*y''' + (x^3)*y'' + 43.2*y = exp(x^2)/atan(x)

is a linear differential equation (y and its derivatives only appear to the power 1 or 0).

On the other hand, the simple differential equation

y' = 1/y

Answer 2

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