Given y1(t) : t2 and y2(t) : t' 1 satisfy the corresponding homogeneous equation of t%\"%F:mi4mt>0 Then the general solution to the non-homogeneous equation can be written as 90?) = Layla) + 62920?) + Y(t)- Use variation of parameters to find Y(t). Use undetermined coefficients to find the particular solution to y"' + 2y' - 8y = 2 sin(3t) Y(t) = 12 cos( 3t ) + 34 sin( 3t X 425The general solution to this ODE: Ay + 4y = e" 2t In(t) is: y ( t ) = 2t 2t Ge + cate +e 2t 12 log ( t ) - X 2An object weighing 8 lbs stretches a spring 7 inches. The object is in a medium that exerts a viscous resistance of A lbs when the object has a velocity of 2 ft! sec. This object-spring system will be overdamped if: A 3 lbs Not every interpretation of direction is that "positive is down". In this problem, assume that if initial position is above equilibrium, then it is positive, and if it is below equilibn'um it is negative. This assumption will have implications on the initial velocity as well. A 9 kilogram mass is attached to a spring whose constant is 10.89 Him, and the entire system is submerged in a liquid that imparts a damping force numerically equal to 45.81 times the instantaneous velocity. Determine the equation of motion if the mass is initially released with a downward velocity of 2 mfsec from 7 meters above equilibrium. 3:05) : ] The differential equation mm\" +m' +ka: = 0 models damped harmonic motion by a spring-mass system in which the damping force is proportional to the instantaneous velocity (with constant of proportionality ,8}. Suppose a spring-mass system is immersed in a viscous medium that exerts a damping force of 51 lbs when the mass has velocity 3 ftlsec. Find the constant of proportionality . 3: l