Complex and Real Fundamental System

Solution Method

For a Complex Solution $y_1(t)$ and $y_2(t)$ The Real Fundamental Solution can be Calculated with the Forms

$$v_1=\frac{y_1(t)+y_2(t)}{2}$$ $$v_2=\frac{y_1(t)-y_2(t)}{2i}$$

Complex Fundamental System = $\{y_1,y_2\}$ Real Fundamental System = $\{v_1,v_2\}$