Answer Happy

The general solution of the homogeneous differential equation y" + ly = 0 can be written as where a, b are arbitrary constants and Ye a cos(x) + b sin(x) = is a particular solution of the nonhomogeneous equation y" + ly = 5e-2x By superposition, the general solution of the equation y" + 1y = 5e-2x is y = y + yp so y =

NOTE: you must use a, b for the arbitrary constants. Find the solution satisfying the initial conditions y = y(0) = 2, y (0) = 3 The fundamental theorem for linear IVPS shows that this solution is the unique solution to the IVP on the interval The Wronskian W of the fundamental set of solutions cos(1x) and sin(1x) of the homogeneous equation is W =