section C, problem 7

7. Solve the heat equation attached. Please do #7 only. Step by step work and explaination and solution, thanks (answer is provided in the attachment..)

section C, problem 8

step by step work and explaination and solution, thanks (answer is provided in the attachment..)

section C, problem 9

step by step work and explaination and solution, thanks (answer is provided in the attachment..)

Heat Diffusion Equation / Standard Heat Equation

a) Let the temperature u inside a solid sphere be a function only of radial distance r from the center and time t. Show that the equation for heat diffusion is now: {see attachment}. This is not an exercise in doing a polar coordinate transformation. First you should derive an integral form for the equation by integrating over an appropriate domain. Then from this obtain the differential equation. b) Show that a transformation of the form {see attachment} for a suitable choice of m can be used to reduce this equation to the standard heat equation

Heat Equation/Moving Source

attached