- #1

- 351

- 81

$$

y’ +ky = k \cos(\omega t)$$

can be solved by replacing cos(ωt) by ##e^{\omega t}## and, rewriting thus,

$$

\tilde{y’} + k\tilde{y}= ke^{i \omega t}

$$

Where ##\tilde{y} = y_1 + i y_2##. And the solution of the first equation is the real part of the solution of the second equation. The purpose to go from first equation to the second is to ease the process of solving.

I believed the transformation, and it also doesn’t seem very alien, but I just want to know more about it. Can Real/Complex analysis prove that the real part of the solution of the second equation is the solution of the first equation?