1. Symbolic analysis via Laplace transform. This will provide a closed-form reference solution.
2. Numerical analysis based on direct solution of the circuit equations formulated in the MNA (Modified Nodal Analysis) form.
3. Numerical analysis based on some off-the-shelf computer program of the SPICE class.
Software tools:
MATLAB/Octave
LTSPICE (free download from [login to view URL])