EDIT: Here is the entire problem from the class website:

Attempt to write each equation in the form , where L is a linear operator. If that is not possible, at least write the equation in the form , where L is an operator (but not a linear operator.)

For the operator L so obtained in each equation, determine whether the linearity condition is true for L:

i) L(f + g) = Lf +Lg

ii) L(cf) = cLF

a) (dy/dx) + x(y)² = 1

b) x(dy/dx) + y = sinx

c) y((d)^2y/d(x)2) + (dy/dx) + xy = 1

d) ((d)^2y/d(t)2) + y² = 0

Part II

Now go back through the problems above, a) – d), and determine whether the given equation is linear or nonlinear; also give the order of each equation.