Trying to solve a first-order differential equation (Ramp Function in a Circuit)

[psychocowtip]

1. I am trying to find i(t) through an inductor in a thevenin-reduced circuit. I come down to the equation di/dt+8i=0.2v(t) where v(t) is the ramp function 4r(t).

2. So the simplified equation is di/dt+8i=0.8t.

3. I found the homogenous equation (i=Ae^(-8t)) but I cannot figure out how to get the particular solution. The initial condition is i(0)=0.

Thanks for any help

 

[vela]

Use the method of undetermined coefficients, or use an integrating factor to solve the differential equation.