Using the separation of variables method, solve clearly IBVP: \text { PDE } u_{t}=u_{x x} \quad 00 \mathbf{B C} u_{x}(0, t)=0, \quad u_{x}(1, t)=0 \quad t>0 \text {

IC } u(x, 0)=x \quad 0 \leq x \leq 1