. Consider the differential equation
(t sin(t) + cos(t))y − t cos(t)y + cos(t)y = 0. (2)
(a) Find and solve a differential equation satisfied by the Wronskian W(y1,y2)(t) of a fundamental set of solutions y1(t),y2(t) for (2).
(b) Check that y1(t) = t is a solution and find another linearly independent solution.
(c) Write down the general solution, and find the solution with (y(0), y′(0)) = (1, 1).