For a continuous function q defined on ℝ, consider the ordinary differential equation (ODE): d2ydx2 + q(x)y = 0, x ∈ ℝ. Which of the following statements is FALSE?

Consider the following statements: (P) The initial value problem y' = f(y), where f(y) = y cos(1/y) for y ≠ 0 and f(0) = 0, with y(0) = 0, has at most one solution. (Q) If z(x) is the solution of the initial value problem z' = (1 - z4)1001 + z2, z(0) = 0, then for each α ∈ (0, 2), there exists xα ∈ &mathbb;R such that z(xα) = 1 - α. Which of the following statements is true?

For the ordinary linear differential equation x2y'' + y' sin x + xy = 0, the point x = 0 is: