Step response for RC circuits. Help >.<

[Axioms]

Hey. Ive been struggling to solve this circuit for a while now.

 

They ask you to find v(t) for t > 0.

 

They get 6.25V for the v(infinity). I have no idea how they get that value. Its a first order circuit so it shouldn't take anyone that long to solve.

 

Ive tried every method that I know of to solve for v(infinity) = 6.25... I just dont get that value.

 

By inspection I would have thought it would be 15V with Rth at 8Ohm.

 

If you could just push me in the right direction, as in how to get the voltage across the capacitor at t = infinity, it would be much appreciated.

 

 

The equation is: v(t)= v(infinity) + (v(0) - v(infinity))(exp(t/tau))

 

tau = RC

v(infinity) = the steady state response

v(0) is the transient response

v(t) is the complete response

 

Image of circuit is attached here:

 

 

[Axioms]

Ok I've solved it. Lol it was actually quite simple but I made it complicated >.<. My mistake when I tried node analysis initially was a sign error over the 5V source. That then took me to try to solve it with differential equations. I made the same sign error there =/.

 

Well this is what I got. Anyone agree with me?