I have two equations and I'm trying to solve $V_2$. The equations are: $$\frac{V_1}{sL}+\frac{V_1-V_2}{R}=I_s,\\ \frac{V_2-V_1}{R}+\frac{V_2}{1/sC} = 0$$
If I solve the second equation with respect to $V_1$ I get: $V_1=V_2 (sRC+1)$
It all goes down hill when I sub $V_1$ into first equation. I end up getting $$\frac{I_s}{\frac{1}{sL}+\frac{sC}{R}} $$
However the correct answer is: $$\frac{s I_s}{C[s^2+\frac{R}{L}s +\frac{1}{LC}]}$$
Can someone help me walk through this step by step to figure out why I am getting the wrong answer.