The rate of change of y with respect to t is proportional to 50-t.

Question

 solve the differential equation

Answer 1

k = proportionality constant

 

dy/dt = k(50 - t)

 

dy = k(50 - t)dt

 

y = ∫dy = ∫k(50 - t)dt = k(50t - t²/2) + c,

 

where c and k are to be determined from initial conditions, which were not stated in the problem

Answer 2

y' = k(50-t)

y = k∫(50-t)dt = 50kt -kt²/2 + C

 

This is the general solution.  In order to evaluate k and C, you need to have initial conditions.