Use Laplace transforms to solve the initial value problems in Problems 1 through 16. 1. x" +4x = 0; x(0) = 5, x'(0) = 0 2. x" +9x = 0; x(0) = 3, x'(0) = 4 3. x"-x' - 2x = 0; x(0) = 0, x'(0) = 2 4. x" +8x' + 15x = 0; x(0) = 2, x'(0) = -3 5. x" +x = sin 2t; x(0) = 0 = x'(0) 6. x" +4x = cost; x(0) = 0 = x'(0) 7. x" +x =cos 3t; x(0) = 1, x'(0) =0 8. x" +9x = 1; x(0) = 0 = x'(0) 9. x" +4x'+ 3x = 1; x(0) = 0 = x'(0) 10. x" +3x' + 2x = 1; x(0) = 0, x'(0) =2 11. x' = 2x + y, y' = 6x + 3y; x(0) = 1, y(0) = -2 12. x' = x + 2y, y' = xte '; x(0) = y(0) =0 13. x' + 2y' + x = 0, x' - y' + y = 0; x(0) = 0, >(0) = 1 14. x" +2x + 4y = 0, y" +x+ 2y =0; x(0) = y(0) = 0, x'(0) = y'(0) = -1