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

False

Let us consider the differential equation $D^2 y=0$ The general solution is: $y(x)=b_1+b_2x$ and $xy(x)=b_1x+b_2x^2$ Let us consider the differential equation $D^4 y=0$ The general solution is: $y(x)=c_1+c_2x+c_3x^2+c_4x_3$ Therefore, the given statement is False.