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Flashcards: Partial Differential Equations

Which of the following describes the physical phenomena that is the biharmonic wave equation?

$u_t-k(u_{xx}+u_{yy}+u_{zz})=0$

$u_{tt}-c^2(u_{xx}+u_{yy}+u_{zz})=0$

$u_{xx}+u_{yy}+u_{zz}=0$

$\bigtriangledown^2u=f(x,y,z)$

$u_{tt}+c^2\bigtriangledown^4u=0$

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Flashcards: Partial Differential Equations

Which of the following describes the physical phenomena that is the biharmonic wave equation?

Your answer:

$u_t-k(u_{xx}+u_{yy}+u_{zz})=0$

Your answer:

$u_{tt}-c^2(u_{xx}+u_{yy}+u_{zz})=0$

Your answer:

$u_{xx}+u_{yy}+u_{zz}=0$

Your answer:

$\bigtriangledown^2u=f(x,y,z)$

Correct answer:

$u_{tt}+c^2\bigtriangledown^4u=0$

Explanation:

When dealing with partial differential equations, there are phenomenons in the physical world that have specific equations related to them in the mathematical world.

Looking at the possible answer selections below, identify the physical phenomena each represents.

$u_t-k(u_{xx}+u_{yy}+u_{zz})=0$ is known as the heat equation.

$u_{tt}-c^2(u_{xx}+u_{yy}+u_{zz})=0$ is known as the wave equation.

$u_{xx}+u_{yy}+u_{zz}=0$ is known as the Laplace equation.

$\bigtriangledown^2u=f(x,y,z)$ is known as the Poisson equation.

$u_{tt}+c^2\bigtriangledown^4u=0$ is known as the biharmonic wave equation.

Therefore, the correct answer for the biharmonic wave equation is

$u_{tt}+c^2\bigtriangledown^4u=0$

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All Partial Differential Equations Resources

Flashcards: Partial Differential Equations

Flashcards: Partial Differential Equations

Flashcards: Partial Differential Equations

Flashcards: Partial Differential Equations

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