Question

Which of the following forms for Y(t) is suitable for finding a particular solution using the method of undetermined coefficients?

A) Y(t)=At²e³ᵗ
B) Y(t)=Ate³ᵗ
C) Y(t)=Ae³ᵗ
D) Y(t)=Asin(3t)

Answer 1

The suitable form of Y(t) for finding a particular solution using the method of undetermined coefficients is Y(t)=Ate³ᵗ. In this method, we assume that the particular solution has the same form as the non-homogeneous term, with some undetermined coefficients.

Step-by-step explanation:

The form of Y(t) suitable for finding a particular solution using the method of undetermined coefficients is B) Y(t)=Ate³ᵗ

In the method of undetermined coefficients, we assume that the particular solution has the same form as the non-homogeneous term, with some undetermined coefficients.

For the equation Y'' + p(t)Y' + q(t)Y = g(t), the particular solution can be found by assuming Y(t) = C(t)e³ᵗ, where C(t) is a polynomial in t of the same degree as g(t).