Chapter 8 - Linear Differential Equations of Order n - 8.1 General Theory for Linear Differential Equations - True-False Review - Page 503: i

True

Plug $y=e^{rx} $ in the given equation. So, $(r^2-3r+2)e^{rx}=0$ This implies that $r^2-3r+2=0 \implies r=1, 2$ and $y=c_1e^x+c_2e^{2x}$ So, basis of $ker(L)={e^x, e^{2x}}$ Therefore, the given statement is True.