I was wondering if someone could check my diff eq I had to solve with an initial condition:

dy/dt + 2y = 1, y(0) = 5/2

MY WORK:

dy/dt = 1 - 2y => dy = (1 - 2y) dt => dt = 1/(1 - 2y) dy

Take integral of both sides:

t = -1/2 * ln|2y - 1| + C

Using the initial condition:

0 = -1/2 * ln|2*0 - 1| + C

0 = 0 + C

Thus C = 0.

And therefore the solution is t = -1/2 * ln|2y - 1|.

Anyone see any mistakes?