Question

how do you identify linear differential equations

Answer 1

lde are linear in y and y' (although they don t have to be linear in t)
hope it helps :)

Answer 2

linear differential equations mean if y1 and y12 are the solutions of a differential equations then c1y1+c2y2 should also be the solution of the equation. where c1 and c2 are any arbitrary integers.this is exact definition of LDE.
now coming to your question how to identify a Differential equation is linear or not?
1.by the definition the equation can take form Ly=f where L is the linear differential operator.
it takes form as mentioned in http://en.wikipedia.org/wiki/Linear_differential_equation.
it cannot have squares of derivatives but it can have linear combination of derivatives of any order.hope this answers this questions