Determine whether the given function is a solution to the given differential equation.

1. x = 2 cos t - 3 sin t, x" + x = 0

2. y = sin x + x^2, d^2y/dx^2 + y = x^2 + 2

3. x = cos 2t, dx/dt + tx = sin 2t

Juanita wade's new car has an msrp of $28,902.11 including title and processing fees. the premier package which includes surround sound and dvd player costs three times the amount of the in-style package which includes leather seats and select wheels. the total cost of her new car was $34,290.08 which included the 6.5% sales tax. find the cost of the premier package to the nearest cent.