so I have the equation: t is time in seconds x represents concentration of a salt in solution

the initial condition being at t=0, x=50

so I used bernoulli's equation substitution then integrating factor I got:

which stops giving realistic values after 2 seconds

also according the the differential equation the concentration should peak around x=200 but with the solution it doesn't so I'm guessing I did something wrong.

So what should I have done?