1. Solve the IVP. (xy2 + 3y2)dy-2xdx = 0 y(-4)=-3/18 2. Solve the IVP. y" +2y+2y=8(t- -플) y(0) = 3, y'(0) = = 0 3. Solve the IVP. Answer in explicit form. State the interval of validity for your solution. x dy sin.x +2y = dx x 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. b. Determine the equation of motion. Determine the first time (after t = 0) when the mass first passes through equilibrium. Solve the IVP. 6. y" - 8y' + 15y = 9te² y(0) = −1, y'(0) = 3 7. Find the general solution of the ODE. 8. x²y" 2y 3x² - 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