1. Solving ODEs with dsolve:
MATLAB has a built in solver for producing the solution to simple ODEs. Two resources are provided for demonstrating how to use this tool.
1. Youtube video on 1st order ODEs and PDF notes for dsolve .
2. Youtube video on higher order ODEs and PDF notes for higher order ODE with dsolve.
Supporting m-files used in videos:
file1, file2, file3, file4, file5, file6, file7.
2. Solving ODEs with ilaplace.m:
MATLAB has tools for handling Laplace transforms which thus can also be used to solve ODEs. Simple examples are given here.
1. Using Laplace with MATLAB: 1st order ODEs
2. Using Laplace with MATLAB: 2nd order ODEs.