In Exercises 53-58, verify that the given function is a particular solu- tion to the specified nonhomogeneous equation. Find the general solu- tion and evaluate its arbitrary constants to find the unique solution sat- isfying the equation and the given initial conditions. x" 53. y" + y' = x, yp x, y(0) = 0, y'(0) = 0 2 54. y" + y = x, yp = 2 sin xx, y(0) = 0, y'(0) = 0 55. - ½y" + y' + y = 4e³ (cos x − sinx), = Ур 2ex cos x, - 56. y" — y' — 2y = - y(0) = 0, y'(0) = 1 - - 1 − 2x, yp = x − 1, y(0) = 0, y'(0) = 1 57. y″ − 2y' + y = 2e*, yp = x²e*, y(0) = 1, y'(0) = 0 - 58. y” − 2y' + y = x¯¹e³, x > 0, = Ур xeln x, y(1) = e, y'(1) = 0