simulate this circuit – Schematic created using CircuitLab
so I have this Op-Amp problem. I need to find for the values of V1, V2 and Vout for t > 0. I have this solution but I'm not sure if I got it right. If not, what part did I have an error?
It's not in the picture but the continuity variables V1 and V2 both have a value of 1 volt. Also, I don't know how to interchange the polarities but the positive terminal of the Op-Amp should be on top. 
Best Answer
No need for all that maths....
A TL081 does not have much output drive and with only 10 ohms to ground the thing is going to struggle to move the output anywhere, I would guess the thing will sit with the output pretty much at ground with the output stage hard in current limiting no matter what you do to the inputs.
Note also that your two schematics are NOT the same, the one on paper has R2/R4 joined at Va, the other one does not, and the inverting/non inverting inputs are swapped between the two if you were to assume an ideal opamp instead of the 081 it would make a difference.
R4 can be replaced with a short circuit without changing anything, and Vout = Vb * (1 + R7/R6) = 2 * Vb.