\section{Ex 3}
The problem number three is solved using MATLAB.  MATLAB has various built in functions for solving ode.  There are both stiff and non stiff solvers in MATLAB.  These solvers are listed below 

\subsection{Non stiff solvers}
\subsubsection{ode45}
ode45 is based on an explicit Runge-Kutta formula.  It is one step solver.  Order of accuracy is medium

\subsubsection{ode23}
ode23 is an implementation of an explicit Runge-Kutta method.  This is also a one step solver.  Order of accuracy is low.  It may be better than ode45 at crude tolerances.

\subsubsection{ode113}
This is  is a variable order Adams-Bashforth-Moulton PECE solver.  ode113 is a multistep solver.  Order of accuracy is low to high

\subsection{Stiff Solvers}

\subsubsection{ode15s}
ode15s is a variable order solver based on the numerical differentiation formulas (NDFs). Optionally, it uses the backward differentiation formulas (BDFs).  Multistep solver.  Order of accuaracy is medium to low.

\subsubsection{ode23s}
ode23s is based on a modified Rosenbrock formula of order 2.   It is one step solver.

\subsection{Answers}
We have used ode15s for solving the problem number three.
\input{p03table}
