This page shows some basic commands for solving ODEs. To see more examples of how to use Sage to solve ODEs (and create graphs and more), see *http://www.sagemath.org/doc/reference/calculus/sage/calculus/desolvers.html
=== Homogeneous ODE Solver === <sagecell> t = var('t') y = function('y', t) ode = diff(y,t,2)+3*diff(y,t)+2*y == 0
desolve(ode, y)
</sagecell>
=== Non Homogeneous ODE Solver === <sagecell> t = var('t') y = function('y', t) ode = diff(y,t,2)+3*diff(y,t)+2*y == t
desolve(ode, y)
</sagecell>