MATH201 Chapter 6: 6 - Partial Differential Equations.pdf

Apply the generalized integral transform method to solve the following system of coupled PDEs 0y1 Ð°Ñ ? B.C I.C If the operator is given by: 0 an solve the vector PDE, L and the eigen value problem, LKn -Kn, finding the components of the kernel, Wn and Dn, and the final solutions for the y1(x, t) and y2(x,t) profiles. Use: (ulv) - u1vx +^u2v2dx to find the inner products in the final inverteod from of the vector solution:

Solve the following electronics applications using any method you choose. Find the current l as a function of time t (in seconds), given that I satisfies the differential equation I' + R/L I = sin(2t). Where R = 550 Ohms, L = 4 Henrys, l(0) = 0. q" + R/L q' + 1/LC q = 1/L E(t) where R is resistance (in Ohms), C is capacitance (in Farads), L is the L LC L inductance (in Henrys), E(t) is the electromotive force (in Volts), and q is the charge on the capacitor (in Coulombs). Find the charge q as a function of time for the electrical circuit described. Assume that q(0) = 0 and q'(0)= 0 R = 20, C = 0.02, L = 2, E(t)=35