The partial differential equation $\frac{\partial \mathrm{u}}{\partial \mathrm{t}}=\alpha \frac{\partial^{2} \mathrm{u}}{\partial \mathrm{x}^{2}},$ where $\alpha$ is a positive constant, is

(A) circular.

(B) elliptic.

(C) hyperbolic.

(D) parabolic.

The partial differential equation $\frac{\partial \mathrm{u}}{\partial \mathrm{t}}=\alpha \frac{\partial^{2} \mathrm{u}}{\partial \mathrm{x}^{2}},$ where $\alpha$ is a positive constant, is

(A) circular.

(B) elliptic.

(C) hyperbolic.

(D) parabolic.

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