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Soln:-given (d^(2)y)/(dx^(2))+9y=0-(1)given ferticylar solutions cos 3x and sin 3xNow we show that c_(1)sin 3x+c_(2)cos 3x is also solution of given differentiol Eqationso let{:[y=c_(1)sin 3x+c_(2)cos 3x],[y^(')=3c_(1)cos 3x-3c_(2)sin 3x],[y^('')=-9c_(1)sin 3x-9c_(2)c ... See the full answer