1.} Find a differential equation whose general solution is y = them + C264\". v 2.} Solve the initial value problem y\" _ 3y} _ 409 = 0} y(0) : CE, yr(0) = _5' Find a so that the solution approaches zero as t > oo. I Determine the values of o, if any, for which all solutions of the differential equation y" - (20 - 12)y' + (a2 - 12a + 27)y = 0 tend to zero as t - co. Also determine the values of a, if any, for which all (nonzero) solutions become unbounded as t - co. There is no value of o for which all solutions will tend to zero as t - co. All solutions will tend to zero as t - co whenever: 09 There is no value of a for which all solutions will become unbounded as t - co. All (nonzero) solutions will become unbounded as t - co whenever: 9If the Wronskian W of f and g is test, and if f(t) = t, find g(t). NOTE: Use c as an arbitrary constant. Enter an exact answer. t pot g0) = + ct 8Find the Wronskian of the functions f(t) = 6et sin(t) and g(t) = et cos(t). NOTE: Your answer must be simplified. W (f, g) (t ) = -6 e2t 6.) Do the functions y, = cost and y, = sinst constitute a fundamental set of solutions of the differential equationy" + 16y = 0? The functions do not constitute a fundamental set of solutions of the differential equation.7.) Find the Wronskian of two solutions of the differential equation thy" - t(t - 3)y' + (t - 6)y =0 without solving the equation. NOTE: Use c as a constant. W (t ) = C 8.) If y, and y2 are linearly independent solutions of ty" + 2y' + telly = 0 and if W(y , y2)(1) = 6, find W(y1, }2)(5). Round your answer to two decimal places. W(1. ))(5) = 0.24