Velocity under friction constrain : differential equation
A body having mass 60 kg slides on the top of a table under a force of 54sin2t N. Force of friction is 60 times its velocity and initially the velocity is zero. Express velocity of the body as a function of time.
Not entirely sure here but by the look of it you have 54Sin2t-60v=m.dv/dt . You could integrate both sides with respect to t to start with.
Just read jim360's contribution (thanks jim) - I omitted to check your profile before answering. I'll know better next time.
Other easiest method is to use D Operator method which is used at graduate level.
the differential equation you stated is correct... But solving it will be tricky as integrating vdt normally by integration by parts would result in recurring never ending integration. So you need to rationalize in some intermediate step with e^x and then try to solve it.
Solution : (9/50)x (sin2t - 2cos2t + 2e ^-t)