If y = A e ^{– kt} cos (pt + c), prove that , where n² = p² + k².

49

If x = a sin t – b cos t, y = a cos t + b sin t, prove that .

50

Find A and B so that y = A sin 3x + Bcos 3x satisfies the equation

52

If , prove that

53

If y = a {x + √x² + 1}ⁿ + b{x – √x² + 1} ^{– n}, prove that (x² – 1) .