What is the error in my analysis?
Somebody already gave you the answer but I can answer your question "what I am doing wrong here?"

For Node 2, you forgot to include the current \$i_x\$ and you also forgot to include the current from the \$5 \Omega\$ branch.   Additionally, you don't need to add the current from the \$100 \Omega\$ branch because that current is going into Node 1.  

For Node 1, you set the equation equal to -4, which implies that there is a constant 4 Amp current going into Node 1, but that is not the case.  You should set that equation to 0.