Second Order Linear PDEs

Practice Questions

Partial Differential Equations › Second Order Linear PDEs

Questions

Which of the following describes the physical phenomena that is the heat equation?

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

Which of the following describes the physical phenomena that is the heat equation?

Solve for the general solution using separation of variables.

Given the following information:

$\u_t=u_{xx} \0\leq x\leq1 \t>0$

$\\text{Boundary Conditions: }\left{\begin{matrix} u_x(0,t)=0\ u_x(1,t)=0 \end{matrix}\right.$

$\text{Initial Conditions: }u(x,0)=cos(\pi x)$

Solve for the general solution using separation of variables.

Given the following information:

$\u_t=u_{xx} \0\leq x\leq1 \t>0$

$\\text{Boundary Conditions: }\left{\begin{matrix} u_x(0,t)=0\ u_x(1,t)=0 \end{matrix}\right.$

$\text{Initial Conditions: }u(x,0)=cos(\pi x)$

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