6. Solve the following boundary-value problem y"+9y=0; y(0)=-1, y() = 1 a. Y=cos3x+sin3x b. Y=-cos3x+sin3x c. Y=cos3x-sin3x d. Y=-cos3x+sin3x 7. Find the particular solution to the following differential equation using the method of variation of parameters: y"+6y'+9y=te73t t4 a. VD -e-3t b. yo =- 7+4 -3t C. yp= t4 7+4 d. yo =12 8. A mass of 4 kg is attached to a spring with a spring constant of 128 N/m. The mass spring system is immersed in a fluid with a damping coerfficient of 48m/s. The mass is pushed downward from the equilibrium position with an initial velocity of 0.8m/s. Find the position of the mass at time t. a. X(t)= 0.2(e -4t-e-8t) b. X(t)= e-4t-e-8t c. X(t)= 0.2(e4t_e8t) d. X(t)= ett-8t 9. In an RLC circuit, L=0. 1 H.R=0.6;0, : CO.4F, and E (t) =60v. Find the charge at time t. Assume the initial charge on the capacitor is OC and the initial current is 7.5A. a. q(t)=-16.125e 3x sin(4x) - 24e -3x cos (4x) b. q(t)=-16.125e-3x sin(4x) - 24e -3x cos (4x)+24 c. q(t)=e73x sin (4x) - 24e 3x cos (4x)+24 d. e3x sin (4x) - 24e-3x cos (4x)+24 10. Find the power series solution for the differential equation y"+3xy"-y=0 with the initial conditions y(0)=2 and y'(0)=0. a. y = x - 5 -X4 - 11 72 by = x2. 5 11 x 6 12 72 c. y = 2+x2+- ~x4 4 11 d. y = 2+x2. 5 11 12 72