The auxiliary equation arising from the given differential equations is:
A.E.: `m^2+60m+500` `=(m+10)(m+50)` `=0`
So `m_1=-10` and `m_2=-50`.
We have 2 distinct real roots, so we need to use the first solution from the table above (y = Aem1x + Bem2x), but we use i instead of y, and t instead of x.
We could have written this as:
since we have 2 constants of integration. We would be able to find these constants if we were given some initial conditions.