(c) Find the values of a where the derivative of the function y=e^{-x^{2}}\left(1-2 x^{2}\right) is zero.

y \frac{\partial U}{\partial y}+2 \frac{\partial^{2} U}{\partial x^{2}}=0 (c) Find the values of the constants A, B, C and k > 0 such that the function u(x, t)=(A \sin (k x)+\cos (k x))(B \sin (2 t)+C \cos (2 t)) solves the wave equation \frac{\partial^{2} u}{\partial t^{2}}-\frac{\partial^{2} u}{\partial x^{2}}=0 subject to the boundary conditions U (0, t) = U(2π, t) = 0, and initial conditions u(x, 0)=2 \cos (2 x), \quad \frac{\partial u}{\partial t}(x, 0)=4 \cos (2 x)