The following partial differential equation is defined for $u: u(x, y)$ $\frac{\partial u}{\partial y}=\frac{\partial^{2} u}{\partial x^{2}} ; \quad y \geq 0 ; \quad x_{1} \leq x \leq x_{2}$ The set of auxiliary conditions necessary to solve the equation uniquely, is

(A) three initial conditions

(B) three boundary conditions

(C) two initial conditions and one boundary condition

(D) one initial condition and two boundary conditions

The following partial differential equation is defined for $u: u(x, y)$ $\frac{\partial u}{\partial y}=\frac{\partial^{2} u}{\partial x^{2}} ; \quad y \geq 0 ; \quad x_{1} \leq x \leq x_{2}$ The set of auxiliary conditions necessary to solve the equation uniquely, is

(A) three initial conditions

(B) three boundary conditions

(C) two initial conditions and one boundary condition

(D) one initial condition and two boundary conditions

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