Question

Question #094f0

Answer 1

Duplicate of

https://socratic.org/questions/find-the-second-solution-of-differential-equation-anyone-please-4

Answer 2

`y= c_1 cos 2t +c_2 sin 2t`

Explanation:

The solution to a second degree DE is determined by the roots of its characteristic equation. In the instant case the characteristic equation of DE is `m^2 +4=0` . Its roots are +2i and -2i, which are distincts and imaginary.

There would be two solutions to DE, `y_1= c_1 cos 2t` and `y_2=c_2 sin 2t`

The general solution would thus be `y= c_1 cos 2t +c_2 sin 2t`. The value of constants `c_1` and `c_2` are determined by the initial values conditions attached to the DE.
*