Consider the ordinary differential equation (ODE): d2ydx2 + cos(x)dydx + sin(x)y = 0. Let φ1(x) and φ2(x) be solutions of the ODE satisfying φ1(0) = 1, φ'1(0) = 0, and φ2(0) = 0, φ'2(0) = 1. Which of the following statements is true?

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: