MATH1350 Lecture 1: math 1350 section 1.2 page 31 explorations with patterns

p = ks, where k is a constant. s = nt, where n is a constant Two relationships involving the variables p, s, and t are given above. Which of the following must be true? p is directly proportional to t. p is directly proportional to t2. p is equal to L. p is directly proportional ro 1/t p is directly proportional to 1/r2. p = ks, where k, :s constant, s = nt, which n is a constant Two relationships involving the variables p, s, and t are given above. Which of the following must be true? p is directly proportional to t. p is directly proportional to t2. p is equal to t. p is directly proportional to 1/t. p is directly proportional to 1/r2.

Solve the boundary value problem by the method of separation of variables: ut = 81 uxx, 0 0, u(0, t) = 0, u(4, t) = 0, t > 0 (Hints: The eigenvalue problem y" + lamda y = 0, y(0) = 0, y(L) = 0 has eigenvalues lamda n = n2pi2/L2 and the corresponding eigenfunctions yn = sin(n pi x/L), n = 1, 2, ... .)

1 point) Take the Laplace transform of the following initial value and solve for Y(s) = L{y(t)) I[ sin(nt), 0