The given partial differential equation (PDE) is Yt = DYxx. This is a second order PDE as the highest derivative is of second order (Yxx).

The classification of a second order PDE can be determined by the discriminant B^2 - 4AC of the general form of second order PDEs, which is Au_xx + 2Bu_xy + Cu_yy + Du_x + Eu_y + F = 0.

In this case, A, B, and C are the coefficients of the second order terms. If B^2 - 4AC < 0, the PDE is elliptic. If B^2 - 4AC = 0, the PDE is parabolic. If B^2 - 4AC > 0, the PDE is hyperbolic.

For the given PDE, Yt = DYxx, we can see that it can be rewritten in the form of the heat equation, which is a type of parabolic PDE. The heat equation is of the form u_t = αu_xx, which is similar to the given PDE.

Therefore, the given PDE Yt = DYxx is a parabolic PDE. So, the answer is C. Parabolic.

Question

The given partial differential equation (PDE) is Yt = DYxx. This is a second order PDE as the highest derivative is of second order (Yxx).

The classification of a second order PDE can be determined by the discriminant B^2 - 4AC of the general form of second order PDEs, which is Au_xx + 2Bu_xy + Cu_yy + Du_x + Eu_y + F = 0.

In this case, A, B, and C are the coefficients of the second order terms. If B^2 - 4AC < 0, the PDE is elliptic. If B^2 - 4AC = 0, the PDE is parabolic. If B^2 - 4AC > 0, the PDE is hyperbolic.

For the given PDE, Yt = DYxx, we can see that it can be rewritten in the form of the heat equation, which is a type of parabolic PDE. The heat equation is of the form u_t = αu_xx, which is similar to the given PDE.

Therefore, the given PDE Yt = DYxx is a parabolic PDE. So, the answer is C. Parabolic.

Knowee AI · Accepted Answer

The given partial differential equation (PDE) is Yt = DYxx. This is a second order PDE as the highest derivative is of second order (Yxx).

The classification of a second order PDE can be determined by the discriminant B^2 - 4AC of the general form of second order PDEs, which is Au_xx + 2Bu_xy + Cu_yy + Du_x + Eu_y + F = 0.

In this case, A, B, and C are the coefficients of the second order terms. If B^2 - 4AC < 0, the PDE is elliptic. If B^2 - 4AC = 0, the PDE is parabolic. If B^2 - 4AC > 0, the PDE is hyperbolic.

For the given PDE, Yt = DYxx, we can see that it can be rewritten in the form of the heat equation, which is a type of parabolic PDE. The heat equation is of the form u_t = αu_xx, which is similar to the given PDE.

Therefore, the given PDE Yt = DYxx is a parabolic PDE. So, the answer is C. Parabolic.

What class of PDE is the equation Yt = DYxx?A. HyperbolicB. EllipticC. Parabolic

Question

Solution

Similar Questions

Upgrade your grade with Knowee