The following partial differential equation is defined for u:u (x, y)  \(\frac{{\partial u}}{{\partial y}} = \frac{{{\partial ^2}u}}{{\partial {x^2}}};y \ge 0; ~ {x_1} \le x \le {x_2}\)

The set 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 conditions and two boundary conditions

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