TITLE: Linear vs nonlinear differential equation
QUESTION [41 upvotes]: How to distinguish linear differential equations from nonlinear ones?
I know, that e.g.:
$$
y''-2y = \ln(x)
$$
is linear, but
$$
3+ yy'= x - y
$$
is nonlinear.
Why?

REPLY [2 votes]: One could define a linear differential equation as one in which linear combinations of its solutions are also solutions.