"By applying Kirchhoff's coltage law to the circuit, you can set up the following expression to figure out how the current will behave after the switch is closed:

V0=IR + 1/C *⌠Idt

To get rid of the integral, differentiate each term:

0=R* dI/dt + 1/C*I or dI/dt + 1/RC*I = 0

This expression is a linear, first-order, homogenous differential equation that has the following solution:

I=I0e^-t/RC"

I cant understand how it arrived to this conclusion, can someone help me?

Thanks.

Edit: I mean how it solved the differential equation that is.