Chapter 8 - Linear Differential Equations of Order n - 8.3 The Method of Undetermined Coefficients: Annihilators - True-False Review - Page 525: h

True

Solve the auxiliary equation for the differential equation. $$D^2+1=0$$ Roots are: $ r_1=i; r_2=-i$ We can see that the roots are in conjugate pair. This implies that the given trial solution is correct. Therefore, the given statement is $\bf{True}$.