Solve this differential equation for y(t)

Question

Let y(t) represent your bank account balance, in dollars, after t years. Suppose you start with $100000 in the account. Each year the account earns 5% interest, and you deposit $4000 into the account.

This can be modeled with the differential equation:

dy/dt=0.05y+4000

y(0)=100000

Solve this differential equation for y(t)

y(t) = 

Answer 1

dy/((0.05y + 4000) = dt; ∫dy/(0.05y + 4000) = ∫dt; 20lnI0.05y + 4000I= t + 20lnC; 0.05y + 4000 = Ce^0.05t;

y(0) = 100000; 5000 + 4000 = C; C = 9000

y(t) = 180000e^0.05t - 80000