Partial Diff. Equarion - Initial Value Problem

Solve the initial value problem.. Please see attached for full question.

Partial Diff. Equation #2

Please solve the initial value problem. See attached file

Partial Diff. Equation #3

Suppose that u(x,t) satisifies the diffusion equation... for 00, and the Robin boundary conditions... where k, L, a0 and aL are all positive constants. Showthat... is a decreasing function of t. Please see attached for full question.

Partiall Diff. Equation. #4

Consider the diffusion equation... Please see attached.

Partial Diff. equation #6

Compute the Fourier series for f on the interval... Please see attached for full question.

Partial Diff. Equation #7

Consider the differential equation...with boundary conditions... Please see attached for full question.

Initial value problem - first order pde - method of characteristics

Please see the attachment for problem statement.

first order partial differential equation - method of characteristics

please see the attachment for problem statement

Diffusion Equation - Energy is a decreasing function of time

Please see the attachment for problem statement.

Heat Equation

Please see attached file