11) Similarity solutions to the Heat conduction equation

Question 1

How do you find the fundamental solution to the heat equation on
−∞ < 𝑥 < ∞ with the integral of u going to 1

Answer 1

Question 2

How do you solve the heat equation with boundary conditions u(x,0) = 0 , u(0,τ) = 1 and u(x,τ) -> 0 as x -> ∞

Answer 2