2. 3. Solve the IVP. y" +2y' + 2y = 8(t- -플) y(0) = 3, y'(0) = 0 Solve the IVP. Answer in explicit form. State the interval of validity for your solution. x- dy sin.x + 2y = dx y(2) = 1 4. 5. Use the method of Frobenius about the regular singular point x = 0 to find the indicial roots and recurrence relation for each root. 2xy" +y+y=0 A mass weighing 16 pounds stretches a spring 3 inches. The medium offers a damping force that is numerically equal to 2 times the instantaneous velocity. The mass is released from equilibrium with a downward velocity of 3 inches per second. a. Determine the equation of motion. b. Determine the first time (after t = 0) when the mass first passes through equilibrium. Solve the IVP. 6. y" 8y+15y9te² y(0)=-1, y'(0) = 3 7. Find the general solution of the ODE. 8. x2y" -2y3x2 - 1 x > 0 Find the general solution of the ODE. y" + 2y 24y = 12x+9-e4x - 9. Solve the IVP. y" +12y" +36y' = 0 y(0) = 0, y'(0) = 1, y"(0) = -7 1