A basic theorem states that a linear differential equation of order n has a general solution that depends on n arbitrary constants. The following examples show that, in general, the theorem does not hold for nonlinear differential equations.
(a) Show that (y')² + y² = 0 is a first-order equation with only one solution y = 0.
(b) Show that (y')² + y² + 1 = 0 is a first-order equation with no solutions.