Nodal analysis with Laplace of simple circuit
I get this set of nodal equations:

$$\begin{align*}
\frac{V_1}{10\:\Omega}+\frac{V_1}{4\:\Omega}&amp;=\frac{V_C}{10\:\Omega}+\frac{V_L}{4\:\Omega}+3\:\textrm{A}\\\\\frac{V_C}{10\:\Omega}+50\:\textrm{mF}\cdot\frac{\textrm{d}\:V_C}{\textrm{d}\:t}&amp;=\frac{V_1}{10\:\Omega}\\\\\frac{V_L}{4\:\Omega}+\frac{1}{2\:\textrm{H}}\cdot\int V_L~\textrm{d}\:t&amp;=\frac{V_1}{4\:\Omega}
\end{align*}$$



Which results in this Laplace matrix:

$$\begin{array}{ccc}
\left[\begin{array}{ccc}
\left(\frac{1}{10}+\frac{1}{4}\right)&amp;\left(\frac{-1}{10}\right)&amp;\left(\frac{-1}{4}\right)\\\\\left(\frac{-1}{10}\right)&amp;\left(\frac{1}{10}+\frac{s}{20}\right)&amp;\left(0\right)\\\\\left(\frac{-1}{4}\right)&amp;\left(0\right)&amp;\left(\frac{1}{4}+\frac{1}{2\: s}\right)
\end{array}\right]&amp;\left[\begin{array}{ccc}V_1\left(s\right)\\\\\\V_C\left(s\right)\\\\\\V_L\left(s\right)\end{array}\right]=&amp;\left[\begin{array}{ccc}3\\\\\\0\\\\\\0\end{array}\right]\end{array}$$



Which yields:

$$\begin{align*}
V_1\left(s\right) &amp;=\frac{30s+60}{s+5} \\\\V_C\left(s\right)&amp;=\frac{60}{s+5}\\\\V_L\left(s\right)&amp;=\frac{30 s}{s+5}
\end{align*}$$



I get the same results. I haven't bothered with the initial conditions, though. Are you taking the initial conditions into account?