The following partial differential equation is defined for $u:u (x,y)$

$$\dfrac{\partial u}{\partial y}=\dfrac{\partial^2 u}{\partial x^2}; \space y\geq0; \space x_1\leq x \leq x_2$$

The set of auxiliary conditions necessary to solve the equation uniquely, is

1. three initial conditions
2. three boundary conditions
3. two initial conditions and one boundary condition
4. one initial condition and two boundary conditions