Obtain the general solution for the following non - homogenous differential equation (use the wronskian method): y - y - 4y + 4y = 12 e - t evaluate the laplace transform of f(t) defined by: f(t) = solve the following initial value problem by using laplace transform: y + 0.2y + 4.01y = where: y(0) = 0 and y(0) = 2 solve the following differential equation: y + y = r(t) where: y(0) = 0 and y(0) = 0 when r(t) is a delayed impulse function given as: r(t) = 4 delta(t - 2 pi). when r(t) is a delayed step function given as: r(t) = u(t - 2 pi). show that the following ode is exact and solve it: cos (x + y) dx + {3y2 + 2y + cos (x + y)) dy = 0 solve the following ode. y' sin 2y + x cos 2y = 2x solve the following ode using integrating factor (x4 + y2) dx - xy dy = 0, y(2) = 1