Our professor introduced the solution of a diffrential equations analogous to polynomials. (Finding roots vs finding functions which satisfied a particular set of operations). While solving 2nd order RLC circuits, I ran into a diffrential equation whose chracteristic roots were equal. My initial thought was that the diffrential equation had the same particular solution (just as a qudratic equation can have same roots). But after doing some googling I found out that it had a second solution (which was pretty unobvious)
Is it an established fact that an ODE have exactly $n$ independent diffrent solutions?