KCL and KVL with Laplace incorrect result
Your equation for \$V_o(s)\$ may be factorised to:
$$\frac{40}{(s+1)(s+6)}=\frac{8}{s+1}-\frac{8}{s+6}$$

Giving:
$$v_o(t)=8(e^{-t}-e^{-6t})$$

The MathCAD answer is also correct (expand it by hand to see), but not in as compact/useful a form.