Chapter 8 - Linear Differential Equations of Order n - 8.2 Constant Coefficient Homogeneous Linear Differential Equations - True-False Review - Page 513: f

True

Let us counter an example: $(D+3)^2(D^2+25)^2y=0$ The four linearly independent solutions to equation are: $y_1(x)=e^{-3x}$, $y_12x)=xe^{-3x}$, $y_3(x)=\cos 5x$ and $y_4(x)=\sin 5x$ The general solution is: $y(x)=c_1e^{-3x}+c_2xe^{-3x}+c_3 \cos 5x+c_4 \sin 5x$ Therefore, the given statement is True.