How to solve Ordinary Differential Equations with Sin(wt) ?

I need to solve an ordinary differntial equation which is non homogenious , how can I got about doing that ?

Answer 1

[Star Strider]

I replaced ‘i’ with ‘c’ to avoid problems with imaginary operators:

syms c(t) w t i0
Eqn = 10*sin(w*t) == 0.001*diff(c) + 100*c;
isol = simplify(dsolve(Eqn, c(0)==i0), 'Steps',100);

That does not affect the solution, that being:

where ‘i0’ is the initial condition.